Two solid metal blocks are placed in an insulated container. If there is a net flow of heat between the blocks, they must have different? 1) Heats...

Heat of fusion is a property of a material telling us how
much energy it will have to gain or release (per gram) to change state between being a
liquid and being a solid. It has nothing to do with the exchange of energy between two
materials when neither changes state, so we can eliminate choice 1 here. Much the same
can be said for choice 3, different melting points. Since there is no change of state in
the scenario, this is not a factor. It is worth noting that the energy required to
change state is often quite different from the energy required to simply change
temperature for a given substance.

Specific heat tells us
how much energy must be absorbed by a substance (again, usually calculated per gram of
material) to change temperature by one degree. While this is relevant to the question,
two blocks of metal with the same specific heat could still exchange energy, providing
they were at different temperatures to begin with. This means that the correct answer to
your question is choice 2, different initial temperatures.