Start by drawing a picture. (Or as well as you can in 3d- I never could draw well!)
The integral you have is
The outer integral has y going from y= 0 to y= 2 so draw two horizontal lines there. The second integral has x going from x= 0 to . The first is the y-axis and the second, since is the same as , is the semi-circle with center at (0, 0), radius 2, and x> 0. This much tells us that goes from to . Finally, is the same as , a cone with which reduces to [tex] which reduces to , and gives , a hemi-sphere with center at (0, 0, 0), radius , and , so .