Olympiad Geometry · Medium problem

In $\triangle ABC$, $D$ is on $\overline{AB}$ and $E$ is on $\overline{AC}$, with $\triangle ADE \sim \triangle ABC$ (sharing $\angle A$). $AD = 3x$, $AB = 12$, $AE = x + 4$, and $AC = 8$. Find $x$.