2021 Pascal Problem 21

Azmi has four blocks, each in the shape of a rectangular prism and each with dimensions 2 \times 3 \times 6. She carefully stacks these four blocks on a flat table to form a tower that is four blocks high. The number of possible heights for this tower is

\textbf{(A)}\ 13\quad \textbf{(B)}\ 14\quad \textbf{(C)}\ 15\quad \textbf{(D)}\ 16\quad \textbf{(E)}\ 17

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 Pascal contests here.