What Black pieces are loose? The knight and rook. Focus on the knight, since it makes a good target for an attack by your own rook. White’s rook can attack the knight in one move (either Rc3 or Rd6). If only the Black king could be pushed onto the same rank or file as the knight; but how? White’s bishop is no help because the king is on the wrong color square. But White has pawns near Black’s king, and pawns are perfect for pushing pieces around by threatening them. Put more simply, what checks does White have? Answer: push a pawn to f4 or h4. Either way the only legal move for Black’s king is onto the sixth rank. When the enemy king is forced to move, you reevaluate what would be possible—what new checks. Answer: Rd6+, winning the knight.

So that’s the forking idea. But actually White has something even stronger. 1. Rd6 threatens to mate next move with h3-h4. Blocking the idea with h5-h4 doesn’t work for Black, because then White has f3-f4+ (forcing the king to h5) and then Bd1#. Instead Black has to reply to 1. Rd6 with Rxa4, using his rook to defend the fourth rank. But then White has BxR and the threat of f3-f4#. Black can fend off the immediate mate threat with f5-f4, but promptly loses his knight to RxN—and now he is out of pieces. The sequence is worth playing through in your mind's eye a few times.