Things look desperate for White: his rook is pinned, and if he plays RxQ, Black mates with Rxe1. Then of course there is White’s battery of queen and rook on the f-file, nearly ready to mate with QxR—but prevented by Black’s queen at the other end of the board. A line of protection so attenuated calls for interference; can White get a piece between Black’s queen and rook? He can, with Ne2 or Ne4. Either move threatens mate with QxR, since the rook on e8 suddenly is loose; RxQ also is threatened, since Black’s reciprocal line of protection running in the other direction—toward e1—is cut off as well. Assume White plays Ne4 and consider Black’s reply options:
(a) If he plays RxN, then of course White mates immediately with Qf8.
(b) If Black plays QxN, White’s rook is unpinned; he mates with 1. Qf8+, RxQ; 2. RxR#.
(c) Best for Black is QxR+, leading to QxQ and the loss of his queen for a rook. It is remarkable what White achieves with a simple move of his knight to the middle of the board.
But what about Ne2 for White instead of Ne4? It seems to accomplish many of the same results: scenarios (a) and (b) above play out the same way. But not scenario (c); for after 1. Ne2, QxRf1+; 2. QxQ, Black has NxN and his knight is protected against recapture by his rook. White ends up trading a rook and a knight for a queen—perhaps a good deal, but of course a failure in view of the decisive gains White can achieve with Ne4. The point is that Ne2, unlike Ne4, puts White’s knight where it can be taken by Black’s.