If a magnetic flux passes through a circular coil when its diameter is D, what should be its diameter (in terms of D) so that only half as much flux passes through it in the same field? Assume that the magnetic field is uniform over the area in both cases.

This really has very little to do with magnetic flux.

You have to realise that because the field is uniform over the area, all you need to work out is how much smaller the diameter must be to halve the area of the circle.

Have a go and let me know if you're still stuck. It's simple geometry.