\(\Rightarrow\) By conservation of charge
\(q_{i}=q_{f}\)
\(Q_{1}+Q_{2}=q_{1}+q_{2}\)
\(4 CV - CV =( C +2 C ) V _{ C }\)
\(v _{ C }=\frac{3 CV }{3 C } \Rightarrow V\)
\(\Rightarrow \frac{1}{2} \times(3 C) \times V_{ c }^{2}\)
\(=\frac{1}{2} \times 3 C \times V ^{2}=\frac{3}{2} CV ^{2}\)