In the free radical bromination of 1-methylcyclohexene using NBS and peroxides a very important consideration to get the appropriate product is:

A. The wavelength of light used for initiation

B. The polarity of the solvent

C. Temperature

D. None of the above

You would need a high enough temperature / low enough wavelength to form the radicals but he said nothing about polarity of the solvent, and there can only be one answer.

From practical experience, I can tell you that the answer is "All of the above".

First, your peroxide initiator needs some energy to undergo homolytic cleavage. This can either be achieved through UV photolysis (A) or heating (B).

$$\ce{RO-OR <=>[h\nu][\mathrm{or\ }\Delta] RO. + .OR}$$

The amount of energy needed will correlate to the strength of the O-O bond. The energy available from UV irradiation is dependent on wavelength because $E=hc/ \lambda$. The amount of energy available from heat is dependent on temperature.

I've initiated NBS reactions both ways, but I prefer heat since I can more easily heat a larger vessel.