What have you tried?

Here's a hint:

1) Draw both polar equations on the same graph from 0 to 2*pi.

2) Find the interval for which R=2 > R=3+2cos(theta), and the interval for which R=3+2cos(theta) > R=2.

3) Try shading the area that is enclosed by both curves, and finding integrals which represent these shaded areas on their intervals.