C _ 1 and C _ 2 are two hollow concentric cubes enclosing charges...

Gauss's law states that the net flux of an electric field in a closed surface is directly proportional to the enclosed electric charge. Therefore,

${ϕ}_{\text{smaller cube}} = \dfrac{2Q}{{ε}_{0}}$

Since the smaller cube is inside the bigger cube, so total charge contained by the bigger cube will be $2Q + 3Q = 5Q$.

${ϕ}_{\text{bigger cube}} = \dfrac{5Q}{{ε}_{0}}$

Therefore, required ratio will be, 

$\dfrac{{ϕ}_{\text{smaller cube}}}{{ϕ}_{\text{bigger cube}}} = \dfrac{2}{5}$.