White’s knight is on a light square. You see a potential fork at e7, but the square is protected by the rook at e6. Can that rook be exchanged away? No, White has nothing attacking it. So is the rook protecting anything else that can be taken? The main thing it is protecting is the other rook at c6; so if that rook could be taken, the rook at e6 would have to move over to recapture, and then the fork at e7 would work. Here as in the previous example, White has a battery of rooks aimed at the critical Black rook on c6. If only the pawn at c5 weren’t in the way. Might it be removed, or simply moved? What is it protecting? The pawn at d4, which is protected twice. So if 1. Bxd4, BxB+; then 2. Rc4xB, c5xR—and finally 3. Rc1xR, RxR. Now at last the fork can be achieved with Ne7+.
Structurally this example is easy enough to understand: the rook on e6 has to be attracted away to c6 for the fork to work; but before c6 can be attacked, two preliminary exchanges are needed to clear the way. What makes it tricky is that each of those initial exchanges involves choices by both sides about which pieces to use—including pieces that you might barely have noticed on initial inspection of the position. For example, if you’re not mindful of all of the pieces on the board it is easy to overlook Black’s bishop on g7 and to imagine that if White plays Bxd4, Black will have to recapture with his c5 pawn. Likewise, if you’re not careful it is possible to overlook White’s second rook on the c-file, and thus fail to see that with the rook on c4 and pawn on c5 out of the way, White will have a clear shot at Black’s rook on c6. The general lesson is not to let any of the pieces on the board drift off your radar screen, and always to ask whether there is more than one way for you or your opponent to capture or recapture in a series of exchanges.
This position is a good example of how to work backwards from a tactical idea to several exchanges needed to make it work. It is worth considering until the train of thought is clear.