A charge Q is situated at the centre of an imaginary hemispherical...

According to Gauss's law, the total electric flux through a closed surface enclosing a charge $Q$ is given by $\Phi_{\text{total}} = \dfrac{Q}{\varepsilon_0}$.

To find the flux through the given hemispherical surface, imagine a complete sphere of the same radius with the charge $Q$ at its center. The hemispherical surface forms exactly half of this complete spherical surface.

By symmetry, the electric field lines emanate uniformly in all directions from the charge $Q$. Therefore, the electric flux through the hemispherical surface is exactly half of the total flux through the complete sphere.

Thus, the flux through the hemisphere is $\Phi = \dfrac{1}{2} \Phi_{\text{total}} = \dfrac{Q}{2\varepsilon_0}$.