White’s more advanced knight has no potential forks except the ineffective Ne6. The less advanced knight at e4, however, is on the same color square as Black’s king and queen, suggesting a fork at f6. The needed square is protected by Black’s bishop at g7, and on inspection you see that the bishop cannot be pinned, captured, or lured away by an attack on one of its protectorates. But imagine proceeding with the fork anyway and allowing BxN; in other words, picture the board with the knight on e4 gone and the Black bishop moved to f6. You are especially interested in whether that sacrifice might make an attack on Black’s king possible, so study its position carefully. Consider any pins that would be in place and any lines that would have been opened by that little exchange. Starting with pins, White’s bishop at c4 already pins Black’s pawn at f7, and still will do so after 1. Nf6+, BxN. As for open lines, the move of the e4 knight would have opened a path for your queen to g6, where it would be possible for you to give a new check (g6 is loose; this is the significance of the pin we just noted).

In reply to 2. Qxg6+, Black would be able to play Bg7 or move his king to h8; either way mate follows with Qh7, since h7 is guarded by White’s remaining knight. So the original fork at f6 wins at least the queen for a knight, and delivers mate if Black is careless.