More fun with knights. The kernel of a discovery for Black should be obvious; his knight on f5 masks an attack that his queen otherwise would have against White’s queen, which is loose. The f5 knight is on a light square and White’s king is on a dark one, so the knight can't give check; but it still might be able to create enough trouble for White’s king to produce the same result. Ask what sort of pressure the knight can put on the White king’s position. By moving to g3 the knight at least cuts off the king’s only flight square: h1. Does this matter? Yes, if Black has another piece he can bring to bear on the king to squash it in its cramped position. Black imagines White replying to Ng3 with QxQ and asks what his next check would be; he sees he would then have the game-ending move Ne2#—another mate with the two knights. So after Black's initial move Ng3 White can’t afford to play QxQ after all. He has to do something to protect his king—e.g., with f2xN, or QxNd4 (followed by Black’s recapture RxQ—after first playing Ng3-e2+ to move his knight to safety with check). One way or another White loses his queen.

When you experiment with initial knight moves for Black, such as Ng3, the important thing to remember is that for now you don’t care if the knight easily can be taken, because then you have QxQ. The question is just whether White can afford to ignore the knight move you are imagining. You answer this by assuming that he does ignore it and then asking what follow-up move you would have.