Here is the same position still one move earlier. The train of thought starts the same, but here there is no way to get the e5 pawn off of its square by attacking something it protects; for it protects nothing. Observe the difficulty of forcing an enemy pawn to move when it protects nothing that you can capture. Don’t give up, though: can you play a forcing move that will cause one of the pawns to then protect something else, creating a way to break the jam? If White somehow could force a Black piece onto d4, then he could take it with his bishop, initiating the sequence described a moment ago. So he experiments with threats; a2-a4 forces the knight to move, and to where? A knight has a maximum of eight places it can move when attacked, and when it’s near the side of the board the number is smaller. Here there are just six squares it can reach, and only one that is available and doesn’t result in immediate capture: Black plays Nd4. And now the stage is set for the sequence examined in the previous problem.
None of this is easy to see. And if you did see it, it might have been as a result not of spotting the forking idea but just of playing with threats and their consequences. You start thinking about a2-a4, see where the knight goes, imagine taking it once it lands on d4, see that this clears the way for a pawn push to e5, observe that Black needs to take the pawn, and then at last come up with the knight fork on e5 at the end. But it's a lot easier to think usefully about these things if you know that you have a potential knight fork lurking on e5 if conditions change. That threat lends structure to the train of thought about your forcing moves and where they lead.
Anyway, look at this position also as another study in the art of getting a bothersome pawn out of your way. If you can force an enemy piece to become a protectorate of the pawn, you can then capture the piece and force the pawn to recapture, moving out of the way.