If this is what your question is :

A charge q is placed at origin. Find the flux through the open plane surface of hemisphere (x-a)^2+y^2+z^2=a^2 ?

Since the surface is the surface of a sphere with radius a and centered at a distance a away from the origin along the x-axis, the sphere does NOT enclose the point charge q. This the net flux through the sphere is ZERO.

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regards

Ramesh