Answer:
5
Step-by-step explanation:
The number of cells in a tile is 4, so the board dimension cannot be odd, but must be a multiple of 2 in order to have the number of cells divisible by 4.
If the tiles are colored in an alternating pattern, tiles must have 3 of one color and 1 of the alternate color. Hence the total number of tiles used to cover a board must be even (so the numbers of each color match). Then the board dimension must be divisible by 4.
In the given range, there are 5 such boards:
4×4, 8×8, 12×12, 16×16, and 20×20
