6. As shown in the figure, in right $\triangle A C B$, $C D$ is the altitude on the hypotenuse $A B$, and $D E$ is the altitude on the hypotenuse $B C$ of $\mathrm{Rt} \triangle C D B$. If $B E=$ $6, C E=4$, then the length of $A D$ is $\qquad$
6. $\frac{4}{3} \sqrt{15}$