With Black’s king stuck firmly in the corner you might naturally think here about mating on the back rank. Qf8 almost would do it for White, but Black’s queen guards the needed square. Don’t stop there; notice also that since the Black king has no flight squares, merely planting a piece on the diagonal leading toward it, as with Qf6, also would be checkmate—except that Black guards f6 with his queen and knight. In view of these threats the Black queen helps prevent, turn your attention to ways you can go after it or take something it protects. Either way you are led to Rxb7.
Observe the difficulty of Black’s resulting position:
(a) His queen is under attack but doesn’t dare defend itself, as QxR results in Qf8# for White.
(b) Another way for Black to try to rescue his queen is by interposing his knight from e8 to c7; but then White renews the threat with RxN. Notice the significance of the Black knight’s move to c7: it stops White’s threat of mate with Qf8, because now the way is clear for Black’s rook to prevent the square regardless of what happens to his queen. On the other hand, one of the defenders of f6—the knight—now has moved away, leaving Black’s queen with sole responsibility for preventing Qf6#. So RxN is just as worrisome for Black as White’s original Rxb7: if Black now recaptures QxR, the f6 square is left loose and White mates soon from there.
(c) Trying to rescue his queen thus is futile, and Black is better off spending his time addressing the mate threat directly by replying to Rxb7 with Ng7. Like the other move of that knight just considered, this clears the back rank for defense of f8 by Black’s rook—plus it blocks the dark-squared diagonal. Then after White plays RxQ, Black has Nc6xR. Not great, but it avoids mate for now.
Again we see the importance of not being satisfied when you identify one near mate. Find all of them; for it may be that at least some ways of fending off the first will expose your opponent to the second (or third, etc.).