White to move and win.
White is down two pieces for a rook. Both sides appear active, but fortunately it is White’s turn so he has the first chance to strike.
There are a couple interesting checks to consider. Perhaps the first check to look at is 1.Ng5+ Kh8 (note that 1...Kh6 is quite brave since it walks into a discovered check if White moves the knight). Unfortunately for White it is not clear how to continue or get closer to Black’s king. The best White has is to try to repeat with 2.Nf7+.
What other check does White have?
At first it may be surprising that 1.Qh6+! wins immediately. The obvious reply for Black is to capture the queen with 1...Bxh6. Can you see how White forces mate from there?
White starts with 2.Ng5+ (double-check), and after 2...Kh8, he has 3.Rh7 mate.
Another interesting try for Black is 1...Kg8. Now White can move his knight and give a discovered check. However, wherever the knight moves, Black can respond with 2...Nxb3+ followed by 3...Qxb2 mate. Instead White must come up with something more forcing.
White should find 2.Qh8+! The point is that after 2...Bxh8, White has a double-check with 3.Nh6+ which is also mate!