jmc

The overlap of the two squares is a smaller square with side length 2, so the area of the region covered by the squares is $2(4\times 4)-(2\times 2)=32-4=28$. The diameter of the circle has length $\sqrt{2^2+2^2}=\sqrt{8}$, the length of the diagonal of the smaller square. The shaded area created by removing the circle from the squares is $28-\pi {\left(\frac{\sqrt{8}}{2}\right)}^2=\boxed{28-2\pi }$.