A charge q is surrounded by a closed surface consisting of an...

According to the Gauss law, the total flux linked with a closed surface is $\dfrac{1}{{ε}_{0}}$ times the charge enclosed by the closed surface.

As we can see from the diagram, the given shape encloses the charge $q$, therefore from Gauss law, we can write total flux $= \dfrac{q}{{ε}_{0}}$.

Now, the plane connecting hemispherical shape & conical shape cuts the charge in two equal parts, therefore flux through the conical part will be exactly half of the total flux value.

Hence, flux through conical part is, $\dfrac{q}{2{ε}_{0}}$.

Therefore,

$n = 3$