Answer
$K_c=37037.0$
Work Step by Step
$[CCl_4]=0.09\ mol/10.0\ L=0.009\ M = [S_2Cl_2]$ by stoichiometry
$[CS_2]=0.12\ mol/10.0\ L-0.009\ M=0.003\ M$
$[Cl_2]=0.36\ mol/10.0\ L-3\times0.009\ M=0.009\ M$
$K_c=[S_2Cl_2][CCl_4]/[CS_2][Cl_2]^3$
$K_c=37037.0$