check the picture below.
so.. simply, get the area of the two circles, with radius of 4, we did that, and get the area of the larger circle with radius of 8, we did that.
now... keep in mind that, the area of the larger circle, includes the area of the two smaller circles, if you subtract the area of the two smaller circles from the larger's one, you're in effect making a hole in the larger circle, and what's leftover, is the shaded region.
