Fomin et al., Mathematical Circles Chapter 4- Pigeon Hole Principle Problem 12. Max. no. of kings that can be placed so no two put each other in check

Question

I found this problem in Mathematical Circles in the Pigeon Hole Principle chapter:

What is the largest number of kings which can be placed on a chessboard so that no two of them put each other in check?

I found the answer to be $16$, and was able to prove it is the maximal case. Here is the arrangement:

I think I've misunderstood, since the answer is $12$. The hint says to divide the chessboard into $2 \times2$ squares, which was how I proved $16$ is the maximal case. Maybe it is asking for an arrangement such that even if one king moves, he can not check the other?