For 2.14, knowing that they could pick the same number, how many choices do each of them have?

On 2.18, start by placing the first checker. In how many ways can you do that? Now that the first checker is placed, you need to choose one of the other squares of the same color for the second checker. In how many ways can you choose this second square?

2.19 and 2.20  will be similar to 2.18 once you figure out how many different ways you have to place the red and black checkers.