-Firstly You should find the impulse response of Vc for given impulses
-Then you know that capacitor acts like short circuit in impulse response .
-You find the impulsive current then find voltage by integrating the current in given t so you can find the impulse response.
-Secondly do the same thing for second input.
-For zero state solution you should convolve your first impulse response with first input waveform and second impulse response with second input waveform.
-Convolve 0 to t which you want to find zero state solution then add zero state solution to zero input solution.
I think this can be helpful.