But I'm getting wrong answer. I have solved the problem the end. You can have a look on the attachment to see the procedure I have followed. Please help me. Thank you.
Where did you get that 0.6 factor? This does not seem to be the correct answer. I think it is:
Vc(t) is 8-8e^(-t/0.2)
That should be calculated using the same R computed as the Thevenin resistance. You find that when you "look" into the circuit where the cap is, short the voltage source and compute the resistance. jim got it right.
I'm not sure what "what is the resistance across the capacitor" means, the question is a bit vague. Does it mean just R2 and R3 or does it also include R1?