Trust me this is the easiest solution for this problem that you may find:
1- Look at the figure and you see that the circle is made of 3 regions.
2- Find the total area: d=6 then r=3 . A= 9 pi .
3- The shaded region to non-shaded region is 2/3 . >>>>>>>>>>>>>>>>>> Check that part. How do you determine that and how accurate is this?
4- (2/3)*9 pi= 6 pi
The answere is 6 pi