The electric field in a region of space varies as $\overrightarrow{E}=\left(\text{3V}/\text{m}\right)x\widehat{i}+\left(\text{4V}/\text{m}\right)y\widehat{j}+\left(\text{5V}/\text{m}\right)z\widehat{k}$.  Consider a differential cube whose one vertex is at $\left(x,y,z\right)$ and the three sides are dx, dy, dz, sides, being parallel to the three coordinate axes

Electric flux through the face of cube located at  x=x parallel to y-z plane is only due to x-component of electric field acting at each point of this plane. x-component of electric field on this plane is $3x\widehat{i}\text{\hspace{0.17em}V/m}$ . Electric flux through this face is $=3\text{\hspace{0.17em}xdy\hspace{0.17em}dz}$ . This is inward electric flux.
Electric flux at the face of cube located at x=x+dx parallel to y-z plane is only due to x-component of electric field acting at each point of this plane. x-component of electric field on this plane is $3\left(x+dx\right)\widehat{i}\text{\hspace{0.17em}V/m}$. Electric flux through this face is$=3\left(\text{x}+\text{dx}\right)\text{\hspace{0.17em}dy\hspace{0.17em}dz}$. This is outward electric flux.
Net electric flux through these two surfaces $=3\left(\text{x}+\text{dx}\right)\text{\hspace{0.17em}dy\hspace{0.17em}dz}-3\text{xdy\hspace{0.17em}dz}$
(Outward electric flux)

Likewise, net electric flux through surfaces parallel to x-z plane and parallel to x-y  plane are   $4\text{\hspace{0.17em}dx\hspace{0.17em}dy\hspace{0.17em}dz}$ and $5\text{\hspace{0.17em}dx\hspace{0.17em}dy\hspace{0.17em}dz}$ respectively. Both of these are outward fluxes.
Total electric flux through the cube  ${\varphi }_{\text{tot}}=3\text{\hspace{0.17em}dx\hspace{0.17em}dy\hspace{0.17em}dz}+4\text{\hspace{0.17em}dx\hspace{0.17em}dy\hspace{0.17em}dz}+5\text{\hspace{0.17em}dx\hspace{0.17em}dy\hspace{0.17em}dz}=12\text{\hspace{0.17em}dx\hspace{0.17em}dy\hspace{0.17em}dz}$
Option (B) is correct, Option (A) is wrong
Since, $\varphi \ne 0$ , the net charge enclosed by the cube is not zero.
Option (C) is wrong, Option (D) is correct