Twelve infinite ling wire of uniform linear charge density ($\mathrm{\lambda }$) are passing along the twelve edges of a cube. Find electric flux through any face of cube.

Consider any wire and assume there are 4 cubes placed around the wire, so flux due to the wire through all four cubes will be $\frac{\mathrm{\lambda }l}{{\mathrm{\epsilon }}_{\mathrm{o}}}$ 

Flux due to single wire through each cube is given by $\mathrm{\varphi }=\frac{\lambda l}{4{\mathrm{\epsilon }}_0}$,

similarly four wires out of twelve will have same contribution and eight will have zero ${\mathrm{\varphi }}_{\text{cube }}=\frac{\mathrm{\lambda l}}{4{\mathrm{\epsilon }}_0}\times 12$

Because of symmetry the flux is equally distributed through all six sides, 

${\mathrm{\varphi }}_{\mathrm{side}}=\frac{1}{6}\times \frac{3\mathrm{\lambda l}}{{\mathrm{\epsilon }}_{\mathrm{o}}}=\frac{\mathrm{\lambda }`}{2{\mathrm{\epsilon }}_{\mathrm{o}}}$