Circles with centers $O$ and $P$ have radii $2$ and $4$, respectively, and are externally tangent. Points $A$ and $B$ on the circle with center $O$ and points $C$ and $D$ on the circle with center $P$ are such that $AD$ and $BC$ are common external tangents to the circles. What is the area of the concave hexagon $AOBCPD$? $\mathrm{(A) \ } 18\sqrt{3}\qquad$ $ \mathrm{(B) \ } 24\sqrt{2}\qquad$ $ \mathrm{(C) \ } 36\qquad$ $ \mathrm{(D) \ } 24\sqrt{3}\qquad$ $ \mathrm{(E) \ } 32\sqrt{2}$