We sometimes have spoken of the importance of looking at any points you have under attack in the enemy camp—points, not pieces, because sometimes your attackers will be trained on significant squares, the occupation of which would permit you deliver a fork or (our concern here) checkmate. Mating squares have been discussed in several places elsewhere; the most common example is a square next to the enemy king at which you already have a piece aimed. If you could land another piece there, it would be mate. There are many variations on the theme. Often the piece that threatens to deliver mate on the attacked square is the queen, but there are other possibilities, especially involving aggressive rooks; and sometimes only one of your pieces is needed to threaten (or deliver) mate, as where landing a piece on the back rank would do the job because the enemy king is trapped there. In any event, mating squares commonly are defended by an enemy piece or two. Capturing such a piece may cause it to be replaced by another that does not have the same defensive powers, and that therefore allows you to end the game a move or two later.
The first important thing is to spot potential mating squares wherever they exist. Our basic techniques for this are two. The first is to look for any of your pieces that attack squares adjacent to the enemy king. The second, which partly overlaps, is to study the enemy king’s position and any constraints on its movement.
White’s mate threat should be obvious enough in the position on the left. Look for pieces trained on squares near Black’s king and you see that White’s queen and bishop are lined up against g7; Qxg7 would mate were it not for Black’s knight on e6. Next step: remove the impediment. White attacks the knight with his rook, so he plays RxN. If Black recaptures with QxR, White mates with Qxg7. Since Black can't afford this he will have to try something else instead, letting White keep the knight.
Aye, White wins more. His rook now attacks Black’s queen; if Black wants to avoid both mate and the uncompensated loss of his queen, he needs to play Nd4. This interposes a knight on the long diagonal, blocking the mate threat; more importantly, after White plays RxQ it allows Black to play the fork Ne2+, winning back his queen on the next move—but then eventually losing his knight. But seeing the first few moves of this sequence is enough for now.