Quadrilaterals & Polygons · Challenge problem

Convex kite $ABCD$ has $AB = AD$ and $CB = CD$. The angle at $A$ is $\angle BAD = 90^\circ$, the angle at $C$ is $\angle BCD = 60^\circ$, and the diagonal $BD$ has length $6$. Find the length of the diagonal $AC$. Give an exact answer.