Sometimes a forking square guarded by an enemy piece can be loosened by taking something else the enemy piece protects; or maybe the other piece it protects can be taken for free, as the enemy concludes that recapturing only results in a more costly fork a move later. We saw lots of examples of this in the chapters on the double attack. Now we can see those studies in fuller context: they all were cases where the guardian of the forking square was overworked. Here are some other examples of how these two concepts—the overworked piece and the double attack—usefully can be combined.
With a knight so deep in Black’s territory the thought of a fork can't be far from your mind in the position on the left. Here Ne7+ suggests itself, but the forking square is guarded by Black’s rook. Meanwhile you also have a rook on the open file leading to the f8 square next to Black’s king—and your knight attacks that square as well, so you almost can mate with Rf8. The problem is that f8 is guarded by Black’s rook. So: your two best offensive prospects both are frustrated by the same enemy piece, suggesting it may be overworked. Try going through with one of the two ideas to see if the other then becomes feasible. Starting with the knight fork doesn’t work; for after Black replies RxN, White has nothing left (he needed both his knight and rook to mate on f8). But if you start with the mating threat Rf8+, Black has to reply RxR—and now the fork Ne7+ does work, because you only needed the one piece to execute it. You win a queen for a rook.