2006 Fermat Problem 10

In the diagram, two rectangles intersect at exactly two points, A and B. The maximum possible finite number of points of intersection of *any* two rectangles is

\textbf{(A)}\ 3\quad \textbf{(B)}\ 4\quad \textbf{(C)}\ 12\quad \textbf{(D)}\ 8\quad \textbf{(E)}\ 6

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.