How to find the potential in region $a<r<b$
I know that the general solution for Laplace's equation is $$V(r,\theta)=\sum_{l=0} \left[A_l r^l +\frac{B_l}{r^{l+1}} \right]P_l(\cos{\theta}).$$
But I don't know how to use the boundary conditions to solve this problem. So how to?