The circumference of a circle is equal to $2\pi r$. Hence:

$2\pi r$ = $6\pi \sqrt{2}$

Divide by $2\pi$:

$r = 3\sqrt{2}$

The area of the whole circle is $\pi r^{2}$. So:

$\pi (3\sqrt{2})^{2} = \pi 9(2) = 18\pi$

At this point, I'm going to cheat. No need calculating more than we need to. Only C and D start with $18\pi$, the full area of the circle. $18\pi$ is somewhere near 54, and the square takes up at least half of that total area. In other words, we'll be subtracting more than 6. 36 is more like it, so D is the answer.