Short answer
Qur'an 6:115 means that no one can stop what God (﷾) has decreed or break what He has promised. It is not a promise that men could never alter the earlier scriptures. The verse says God's (﷾) word is fulfilled in truth and justice, so it is about His word coming true. The early scholar Qatadah explained it as truth in what God (﷾) stated and justice in what He decided. Ibn Kathir explains "none can change His words" as meaning no one can turn back God's (﷾) judgement. The Qur'an uses the same phrase for God's (﷾) promise to help His messengers. And the same Qur'an says plainly that men did change scripture. They wrote the Book with their own hands and moved words from their places. Islam's answer: the only book God (﷾) promised to guard is the last one.
Full explanation
The Christian argument
Christians point out that Muslims accept the Torah (the book God (﷾) gave Moses) and the Injil (the Gospel Jesus preached) as God's (﷾) word. If none can change God's (﷾) words, they argue, then the Bible cannot have been corrupted. They say the Qur'an has contradicted itself.
“The word of thy Lord doth find its fulfilment in truth and in justice: None can change His words: for He is the one who heareth and knoweth all.”
What "his words" means here
The verse speaks of God's (﷾) word being fulfilled, that is, coming true. The early scholar Qatadah (8th century) and the commentator Ibn Kathir (14th century) both read it this way. God's (﷾) statements are true, His decisions are just, and no one can turn back His judgement. The verse before it speaks of the Book sent down to the Prophet (ﷺ), explained in detail. So where the words mean a book, the book meant is the Qur'an, which God (﷾) promised to guard. So too in 18:27: "none can change His Words" follows "what has been revealed to thee of the Book of thy Lord", the Qur'an.
“The word of thy Lord doth find its fulfilment in truth and in justice: None can change His words: for He is the one who heareth and knoweth all.”
Explains "fulfilled in truth and in justice" through Qatadah: truth in what God has stated and justice in what He has decided. Explains "none can change His words" as: no one can turn back God's judgement, whether in this life or in the Hereafter. On "never be then of those who doubt" (6:114) he compares 10:94 and explains that it is a conditional statement, which does not mean that doubt ever occurred to the Prophet (ﷺ).
“Say: "Shall I seek for judge other than Allah? - when He it is Who hath sent unto you the Book, explained in detail." They know full well, to whom We have given the Book, that it hath been sent down from thy Lord in truth. Never be then of those who doubt.”
“And recite (and teach) what has been revealed to thee of the Book of thy Lord: none can change His Words, and none wilt thou find as a refuge other than Him.”
The same phrase elsewhere in the Qur'an
The Qur'an uses the same phrase in 6:34: "there is none that can alter the words (and decrees) of Allah". There it means His promise of help to His messengers after long patience. A matching phrase in 10:64 is for His glad tidings to the believers. In each place it means that His promise will not fail.
“Rejected were the messengers before thee: with patience and constancy they bore their rejection and their wrongs, until Our aid did reach them: there is none that can alter the words (and decrees) of Allah. Already hast thou received some account of those messengers.”
“For them are glad tidings, in the life of the present and in the Hereafter; no change can there be in the words of Allah. This is indeed the supreme felicity.”
The Qur'an says men did change scripture
The Book that says none can change God's (﷾) words also says that men wrote a book with their own hands and called it God's (﷾). It says they moved words from their places and twisted the Book with their tongues. It says a party of them altered God's (﷾) word after they had understood it. The Qur'an cannot mean in 6:115 the opposite of what it says in these verses.
“Then woe to those who write the Book with their own hands, and then say:"This is from Allah," to traffic with it for miserable price!- Woe to them for what their hands do write, and for the gain they make thereby.”
“Of the Jews there are those who displace words from their (right) places, and say: "We hear and we disobey"; and "Hear what is not Heard"; and "Ra'ina"; with a twist of their tongues and a slander to Faith. If only they had said: "What hear and we obey"; and "Do hear"; and "Do look at us"; it would have been better for them, and more proper; but Allah hath cursed them for their Unbelief; and but few of them will believe.”
“There is among them a section who distort the Book with their tongues: (As they read) you would think it is a part of the Book, but it is no part of the Book; and they say, "That is from Allah," but it is not from Allah: It is they who tell a lie against Allah, and (well) they know it!”
“Can ye (o ye men of Faith) entertain the hope that they will believe in you?- Seeing that a party of them heard the Word of Allah, and perverted it knowingly after they understood it.”
The Bible's own prophet made the charge too
Jeremiah, a prophet of the Bible who lived around 600 BC, accuses the people of perverting God's (﷾) words. They claimed to have the Lord's law. But the false pen of the scribes, he says, has made that claim a lie. A Muslim who says the scripture was changed makes a charge like Jeremiah's. Jeremiah made it against the scribes of his own day.
“And the burden of the Lord shall ye mention no more: for every man’s word shall be his burden; for ye have perverted the words of the living God, of the Lord of hosts our God.”
““ ‘How do you say, “We are wise, and Yahweh’s law is with us?” But, behold, the false pen of the scribes has made that a lie.”
The one book God (﷾) promised to guard
The earlier scriptures were placed in the care of their people. Only of the Qur'an, the last revelation, does God (﷾) say that He Himself will guard it from corruption. So a Muslim holds the Qur'an to be unchanged and the Bible to be partly changed, without any contradiction.
“It was We who revealed the law (to Moses): therein was guidance and light. By its standard have been judged the Jews, by the prophets who bowed (as in Islam) to Allah's will, by the rabbis and the doctors of law: for to them was entrusted the protection of Allah's book, and they were witnesses thereto: therefore fear not men, but fear me, and sell not my signs for a miserable price. If any do fail to judge by (the light of) what Allah hath revealed, they are (no better than) Unbelievers.”
“We have, without doubt, sent down the Message; and We will assuredly guard it (from corruption).”
Verse by verse
Qur'an 6:115 — Surat al-An'am (The Cattle), verse 115
“The word of thy Lord doth find its fulfilment in truth and in justice: None can change His words: for He is the one who heareth and knoweth all.”
Cited for
None can change God's words, so the Torah and the Injil cannot have been changed.
The response
The verse is about God's (﷾) word being fulfilled: what He decrees happens and what He promises comes true. The Qur'an uses the same phrase for His promises in 6:34. It also says that men wrote a book with their own hands and called it God's (2:79). It says they moved words from their places (4:46).
Where it lands — The verse is about God's (﷾) decrees, not about copies of scripture, so it does not show that the Bible was never changed.
Perspectives
Christian argument
Muslims accept that God gave the Torah and the Injil. If no one can change God's words, the Bible cannot have been corrupted. So the Muslim charge of corruption goes against the Qur'an itself.
Christians read "none can change His words" as a promise that no scripture from God could ever be altered.
Rebuttal
Islam agrees that God (﷾) revealed the Torah (5:44), but 6:115 is about His word coming true, as in 6:34. The same Qur'an says some perverted the Word of Allah knowingly (2:75) and wrote a book with their own hands (2:79). God (﷾) promised to guard only the Qur'an (15:9); the earlier books were left in their people's care (5:44).
The Islamic perspective
In 6:115 God's (﷾) words are His decrees and promises, which no one can stop. The Qur'an says in the plainest terms that people altered the earlier scripture. It promises protection only for itself.
The verse speaks of God's (﷾) word being fulfilled in truth and justice. That is the language of decrees and promises.
Qatadah and Ibn Kathir explain the verse as God's (﷾) true statements and just decisions. No one can turn them back.
The Qur'an uses the same or a matching phrase for God's (﷾) promises to His messengers and to the believers.
The Qur'an states that some people wrote scripture with their own hands, displaced words, and altered God's (﷾) word knowingly.
Jeremiah accused his people of perverting the words of God (﷾). He said the false pen of the scribes had made a lie of their claim to have the Lord's law.
God (﷾) promised to guard the Qur'an itself from corruption. He made no such promise for the copies of earlier books.