Hi there!
Recall the equation for electric flux:
[tex]\Phi _E = \oint E \cdot dA = \frac{Q_{encl}}{\epsilon_0}[/tex]
Assuming a charge enclosed by a cube, we know the total electric flux is equal to:
[tex]\Phi_E = \frac{Q_{encl}}{\epsilon_0}[/tex]
Since there are 6 faces for a cube, we know that each face has 1/6th of the flux passing through it.
Therefore, the amount of flux going through EACH face is equal to:
[tex]\Phi_E = \frac{1}{6}\frac{Q_{encl}}{\epsilon_0} = \boxed{\frac{Q_{encl}}{6\epsilon_0}}[/tex]
