The first hint is just a warning what you shouldn’t do.

External electric field is inducing dipoles on each of the spheres, but the dipole-dipole interaction cannot give rise to any torque to the dumbbell as a whole, due to Newton’s 3rd law: torque from a closed system on itself must be zero! If you obtain from dipole-dipole interaction a non-zero torque, it means that you have missed some contributions to the torque. (This mistake was made in too many solutions.)

Second, be very careful with the numerical factors and double-check – there are many ways how you can go wrong. For instance, you may forget that there are two balls; when using virtual displacement approach and taking derivative of the full energy, you may easily get an extra factor of 2 if you differentiate dipole moments, too.