In these types of problems, you divide the area that you want to get by the area that is whole. Since the smaller circle has diameter of 4 its radius is 2 thus its area is . And the total area which is your big circle has diameter of 8 thus, radius of 4 thus, area of Now divide them thus, . Thus probability is 25%. Since you are throwing 20 darts 20% of them should hit the region thus 20% of 20 = 5.
Do you want to try the second one by yourself?