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(C) The total charge enclosed by the cube is $Q_{	ext{enclosed}} = -q + 3q - q = q$.According to Gauss's Law,the net electric flux through the entire

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$(A, C, D)$

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(C) The total charge enclosed by the cube is $Q_{	ext{enclosed}} = -q + 3q - q = q$.According to Gauss's Law,the net electric flux through the entire closed surface is $\phi = \frac{Q_{	ext{enclosed}}}{\varepsilon_0} = \frac{q}{\varepsilon_0}$. Thus,option $(C)$ is correct.The charges are located on the $y$-axis at $(0, -a/4, 0)$,$(0, 0, 0)$,and $(0, a/4, 0)$.Since the charge distribution is symmetric with respect to the $yz$-plane $(x=0)$,the flux through the plane $x = +a/2$ must be equal to the flux through the plane $x = -a/2$. Thus,option $(A)$ is correct.The charge distribution is not symmetric with respect to the $xz$-plane $(y=0)$. The charges are located at $y = -a/4, 0, a/4$. The plane $y = +a/2$ is closer to the charge at $y = +a/4$ than the plane $y = -a/2$ is to the charge at $y = -a/4$. However,by calculating the flux,one finds the flux through $y = +a/2$ and $y = -a/2$ are actually equal due to the specific arrangement of charges. Thus,$(B)$ is incorrect.By symmetry of the charge distribution with respect to the $xy$-plane $(z=0)$,the flux through $z = +a/2$ is equal to the flux through $z = -a/2$. Comparing this to the flux through $x = +a/2$,we find they are equal. Thus,$(D)$ is correct.

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