Is it possible to transfer heat from a cold reservoir to a hot reservoir?
a.) yes, this transfer process will happen naturally.
b.) yes, if work is done, this transfer process can take place.
c.) yes, it is theoretically possible to transfer heat from a cold reservoir to a hot reservoir, but this has not yet
been accomplished experimentally.
d.) no, it is not possible to transfer heat from a cold reservoir to a hot reservoir.

Answer is: B.) Yes, if work is done, this transfer process can take place.

For example,  air conditioner involves a cyclic process that transfers heat from a cold reservoir to a hot reservoir, but with use of electricity.

Thermal conductuction is the transfer of heat through physical contact. Thermal conduction is the transfer of heat by microscopic collisions of particles. Heat spontaneously flows from a hotter to a colder body.

The process of heat conduction depends on four basic factors: the temperature gradient, the cross section of the materials involved, their path length and the properties of those materials.

the answer to this question is 3.