When you consider the checks you can give, it's important to be thorough in thinking about all of your pieces—and pawns. Here White can check with his g-pawn: g2-g4+. Black can’t retreat the king to h6 because White’s queen attacks the square. He can’t interpose anything because there's no room for that. He has no choice but to capture the threatening pawn with Rxg4 (Kxg4 is made impossible by White’s king). The salient fact on the board as it would then look is that Black's rook ends up on the same diagonal as his king. White has a pin with Qf3. The queen takes the rook next move, safe against recapture because of the protection it gets from White's king.
Incidentally, there is another interesting way for White to win a rook here. Notice that the Black rook on b4 is loose. A loose enemy piece, an exposed enemy king, and a queen at your disposal to attack them: these all are makings of a fork; you need just to look for checking sequences that allow you to maneuver your queen into position. First comes Qf3+, forcing Kh6. Now another check: Qe3+, forcing Kg7 (if Black plays Kh5 or g6-g5, White mates with his queen on g5). Now White has the fork Qc3, picking up the rook next move.