Conduction is the transfer of energy (in this case heat) from one substance to another substance through direct contact. This definition rules out the option D which suggests that heat does not travel between objects of different temperatures.
It is also impossible for heat to be transferred from a cooler object to a hotter object (as claimed in option B) because the atoms in hotter objects are more energized than cooler objects and are hence able to pass there energy to the cooler object whose atoms in less energized or in a relaxed state if cold. This reason also rules out option A because the hotter object contains more energized particles and hence energy (heat) cannot be passed from the cooler object nor can the heat travel in both directions.
From the explanation in the previous paragraphs, it is clear that energy transfer in solids occurs when heat travels from the hotter object to the cooler object via conduction.
