According to Gauss’s Law, the total electric flux ($\Phi$) through a closed surface is equal to the net charge enclosed by the surface ($q_{enclosed}$) divided by the permittivity of free space ($\epsilon_0$). Mathematically, $\Phi = \frac{q_{enclosed}}{\epsilon_0}$ . The flux does not depend on the shape or size of the surface, nor on the distribution of charges inside it; it depends solely on the net magnitude of the enclosed charge . Charges located outside the surface S do not contribute to the net flux through it. Since the probable answer is $2q/\epsilon_0$, it implies that the net charge enclosed within the surface S in the corresponding diagram is $2q$.