If a charge q is placed at the centre of a closed hemispherical non-conducting surface, the total flux…

Assume a complete sphere, then flux due to a charge placed at the center of sphere is $\varphi =\frac{q}{{\epsilon }_0}$

Flux through hemisphere surface is equal to flux passing through flat surface $\varphi =\frac{1}{2}\times \frac{q}{{\epsilon }_0}=\frac{q}{2{\epsilon }_0}$