Start by examining every check. There are two: Qe6 and (less obviously but critically—examine every piece!) Bd5. Qe6+ loses the queen to NxQ. Bd5+ is more interesting. The bishop can’t be taken by any of Black’s pieces, and Black can’t move his king to h7 because of White’s knight. So Black has to play Kh8 (actually he does have one other option we will consider in a moment, but let it pass for now). Now ask how the resulting board would look, and see that it would invite a fork of king and queen via Nf7+. Again, you might have been helped along in seeing this by observing from the start that White can attack the Black queen with one move of his knight and wondering whether Black’s king might be forced by a check onto the dark square at h8 where it could be forked.

As noted, Black has one alternative to moving his king to h8 in response to Bd5+: he could interpose his f8 knight by playing it to e6. But if you ask what checks White then would have, you see that in addition to BxN+ he now has the better move QxN+, capturing the knight that had previously prevented him from checking with his queen. This would again force Black’s king back to h8 and allow White's knight fork on f7. (With his own knight out of the way, Black also would have the option of playing Kf8, but this leads to mate on the move for White with Qf7).