Figure 4.3.5.4[Black to move]

A look at the White king’s position and the constraints on its movement shows that it is stuck on the back rank with no defenders there (a rook is a usual defender against a back rank mate; but White’s rook on a1 is blocked by his bishop). This means that if Black could drop a queen or rook onto the middle of the back rank, he might mate. The most plausible piece for the purpose would be his queen on d3, so ask what prevents Qd1#. There are two things: the pawn in the way on d2, and the knight on e3 that protects d1. A “pawn in the way” is a pawn that is pinned, and this also is the key to dealing with the knight: it is protected by that same pawn, so Black is free to take it with RxN. If White recaptures d2xR, Black plays Qd1#. What about the other pawn that protects the knight—the one on f2? It is pinned as well by the rook on f8.

One way to come at this position in the first place is with a study of the White king’s lines. You see that the pawn in front of it is pinned, and so inspect any pieces the f2 pawn is supposed to protect; you find the knight on e3; you consider taking it with RxN, and ask about the consequences; you see that d2xR could result; you observe that this would clear the way for Qd1#. So both pawns that guard White’s knight are pinned, which makes it free for the taking.

The general point is cognitive. It's natural to see the d2 pawn and e3 knight here and conclude that they are insuperable obstacles to mate. And they are. But train your mind to regard the obstacles not as frustrations but as opportunities. If they really have such powerful defensive roles, this also implies that they may not be able to move and so may signify other vulnerabilities.