Step 1: Structure of crystalline AlCl$_3$.
Solid AlCl$_3$ has a layer-type structure similar to AlBr$_3$. Each Al atom is bonded to 3 Cl atoms in a trigonal planar arrangement. Thus, its coordination number is 3. Step 2: Structure of liquid AlCl$_3$.
On melting, AlCl$_3$ dimerizes to form Al$_2$Cl$_6$, where each Al atom achieves octahedral coordination through bridging chlorides. This raises the coordination number to 6. Step 3: Conclusion.
Hence the coordination numbers are 3 (solid state) and 6 (liquid state).