To find the driving point-impedance do I need to do mesh analysis?
Or is there other techniques to solve the problem?
Welcome to the PF.
I moved your thread from the EE forum to the Homework Help forum because it is askig about schoolwork. Please post schoolwork-type questions here in the HH forums going forward.
On your question, this circuit is simple enough that you can use parallel and serial combination simplification to form the equivalent 2-termianl circuit. That will give ou the drive point impedance. Can you show us that work?