What is the initial condition of the current in the capacitor
Hint: At \$t=0^+\$ what's the voltage across the 6-ohm resistor? Therefore how much current is flowing through it?

And what's the voltage across the 3-ohm resistor? Therefore how much current is flowing through it? 

Using those results and KCL, you can get the current through the capacitor.

Alternative solution, what is the Thevenin equivalent circuit of the source and two resistors? Given the voltage across the capacitor at \$t=0^+\$, what then is the current through the capacitor?