In the figure, $\overline{LQ}$ intersects $\overline{MP}$ at point $R$, and $\overline{LM}$ is parallel to $\overline{PQ}$. The lengths of $\overline{LR}$, $\overline{RQ}$, and $\overline{MR}$ are 8, 12, and 6, respectively. What is the length of $\overline{RP}$?