jmc

We find $CE$ by first finding $BE$.

Since $AE=24$ and $\angle AEB=60^{\circ }$ and $AEB$ is a right triangle, then we can see that $AE$ is the hypotenuse and $BE$ is the shorter leg, so $BE=\frac{1}{2}\cdot 24=12.$

Likewise, since $BE=12$ and $\angle BEC=60^{\circ }$, then $CE=\frac{1}{2}\cdot 12=\boxed{6}$.