Olympiad Geometry · Easy problem

Lines $\ell$ and $m$ are parallel. Two transversals cross at point $P$ between them, forming $\triangle PAB$ (with $A$ on $\ell$) and $\triangle PCD$ (with $C$ and $D$ on $m$), where $A$, $P$, $C$ are collinear and $B$, $P$, $D$ are collinear. If $PA = 6$, $PC = 15$, and $PB = 8$, find $PD$.