Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is :

Use Gauss law.

Charge at center of face CDEF:

It lies exactly on surface of cube.

A charge on a face contributes half its flux through the cube.

So contribution:

$$\Phi_1=\frac{q}{2\epsilon_0}$$

Charge 2q is at vertex A.

A vertex is shared by 8 identical cubes.

So this cube gets one-eighth contribution:

$$\Phi_2=\frac{2q}{8\epsilon_0}=\frac{q}{4\epsilon_0}$$

Total flux:

$$\Phi=\Phi_1+\Phi_2$$

$$=\frac{q}{2\epsilon_0}+\frac{q}{4\epsilon_0}$$

$$=\frac{3q}{4\epsilon_0}$$