On a $3\times3$ grid we have:
with $8$ moves needed to swap the red and blue knights.
What is the minimum numbers of moves to swap the knights on a $4\times4$ grid?
It will take:
20 moves to swap the knights
This can be done as follows:
All credit goes to @klm123 for demonstrating a good way to visualize this in a similar puzzle.
I believe it is, in chess terms,
20 half moves, or 10 move pairs.
In algebraic notation:
1. N3b2 N2c3 2. Na1 Nc1 3. Nb3 Nbd3 4. Ncb4 Nc2 5. N1d2 Nd4 6. Nb1 Nd2 7. Na3 Ncb1 8. Nbc4 Nac3 9. Ndb2 Nc2 10. Na4 Nd1