I've got it! This was a tricky one. At first you're fooled by the lack of material. You're discouraged from allowing Black to take White's bishop, because you know that usually, a knight and a king are not enough material to finish the job. But we get to use Black's pawns to his disadvantage, and that's exactly what we do here...

1. Nc5  Kxg6
2. Nd7  Kh6
3. Ne5  g6
4. Nf7#