In parallelogram $ABCD$, $\overline{DE}$ is the altitude to the base $\overline{AB}$ and $\overline{DF}$ is the altitude to the base $\overline{BC}$. [Note: Both pictures represent the same parallelogram.] If $DC=12$, $EB=4$, and $DE=6$, then $DF=$

$\text{(A)}\ 6.4$$\text{(B)}\ 7$$\text{(C)}\ 7.2$$\text{(D)}\ 8$$\text{(E)}\ 10$