smc

Since Circle $I$ is tangent to circle $II$ and touches the center of circle $II$, the diameter of circle $I$ is the radius of circle $II$. That means circle $II$ is twice as big as circle $I$, so the area of circle $II$ is four times as big as circle $I$. The area of circle $II$ is $16$ square inches, so the answer is $\boxed{16}$.