Two spherical, nonconducting, and very thin shells of uniformly distributed positive charge Q and radius d are located a distance 10d from each other. A positive point charge q is placed inside one of the shells at a distance d/2 from the center, on the line connecting the centers of the two shells, as shown in the figure. What is the net force on the charge q?

All the spherical shells are NON-conducting. 

Hence, there will not be any re-arrangement of charges. The charge distribution will remain as it is given in the question.

The field inside the shell will be zero, so the only field acting at the point of charge Q will be the field due to the shell at 9.5d distance.

Electric field at the location of charge = $\frac{1}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}}\frac{\mathrm{Q}}{(9.5\mathrm{d}{)}^2}$

Force on the charge q is given by q x E.

$\mathrm{F}=\frac{\mathrm{qQ}}{361{\mathrm{\pi \epsilon }}_0{\mathrm{d}}^2}$, as both the charges are positive the nature of force will be repulsive.