you should calculate the volume enclosed by the two spheres and then subtract this volume from the volume of the sphere .to find the volume of the area inside the sphere x2+y2+z2=4z but outside the sphere x2+y2+z2=4.
To get the enclosed volume:
First draw a simple diagram diagram. Looking at it side-one in the xz-plane (y = 0) it's not hard to see that the top surface is and the bottom surface is . This supplies the z-integration terminals.
The x and y integration terminals define the region in the xy-plane defined by the circle .
So integrate the triple integral first with respect to z and then switch to polar coordinates.