Figure[White to move]

Start with a look at your attacking options. You have one principal capture to consider (QxN) and three pieces all trained on Black’s back rank but not quite coordinated (they attack different squares). What should strike you is that Black’s queen is serving more than one defensive purpose. It protects the knight on e5; it also protects d8 from occupation by White’s rook. So think a little more about what the rook could do if Black’s queen weren’t there because White had played 1. QxN, QxQ. You see that 2. Rd8+ then is safe, and it gives check; Black has no good interposition (there is just Qe8, which loses his queen), so he would have to move his king to e7. Ask about the next check you might give. One would be Re8+, which achieves the coordination of White’s rook and bishop that was impossible on White’s first move. As you consider Black’s choices in reply, don’t think about the queen you now have on f5; the premise of this train of thought is that it would have been replaced by Black’s queen. But do notice the knight on e4, which would continue to seal off d6 and f6 as flight squares. Indeed, 3. Re8+ leaves Black’s king with no moves and thus is mate.

So at least at first it looks like White can take the knight on e5. With the idea now clear, go back and make sure it works; in other words, ask whether the Black responses you are counting on really are forced—and if not, what his alternatives are. White’s initial 1. QxN not only captures a piece but also threatens mate (Qe8#), so Black can’t ignore it; but he doesn’t have to reply QxQ. He can play Qc8, taking his queen out of danger and defending the mating square e8. But that's okay; White has won a piece.