you have a 20 x 20 area and you have 4 14 foot fences plus 4 4 foot fences and you need to house 9 dogs and none can be together how do you do it?

Assuming the 20x20 area is enclosed, it's very convenient that the diagonal is 28 feet.

Lay two diagonals, and then cut off each corner with a 4'fence. That gives 12 enclosures, 8 of which are quite small.

If the area is unbounded, there's no reason to specify that it's 20x20.