1. Ka6! g4, 2. Ng5 g3, 3. Ne6 g2, 4. Nc7#

or

1. Kc7! g4, 2. Nf4 g3, 3. Nd5 g2, 4. Nb6#

There are two solutions, by the way.

I knew there was a likely win, but it took me some time to figure it out! On such puzzles, I am usually not guilty of thinking in 1 dimension, but spent too much time trying to bring the second knight to c7 to deliver the mate. This was a nice puzzle!