Look for patterns in the layout of White’s pieces or for threats you can make; the result either way should be to see Black's potential pawn fork d4-d3. The problem is that once the pawn arrives on the forking square it would be attacked twice—by White’s queen and rook—and protected only once, by Black’s rook at d8. So the pawn gets taken if it steps forward. Yes, but let that sequence play out in your mind’s eye: 1. …d3; 2. Rxd3, RxR; 3. QxR, and now what would be possible on the resulting board? White’s queen and knight would be arranged for the fork e5-e4, winning the knight at f3. In effect the initial fork was just another threat that drew the White rook, then (after an exchange) the White queen, into position for a different fork.
Incidentally, note the importance of Black playing the exchange RxR, QxR before executing the fork at the end. If Black plays the pawn fork against White’s rook and knight after the rook has moved to d3, White breaks out of it with RxR+. Once the rook has been replaced with White’s queen, however, White has no good way to break out of the fork. The general points are (a) to always ask whether you can improve the target of a double attack with another exchange, and (b) to always consider what your opponent’s best reply to the fork would be; he may have a check or threat that would enable him to break it—especially if his king is not one of the parties to the fork.