Heat transfer through a solid material like a metal tube wall occurs by conduction.
Conduction is the transfer of heat within a solid or between solids in direct contact.
In refrigeration or air conditioning coils, heat moves through the metal tubing wall by conduction.
Then, convection carries heat to or from the fluid inside or outside the tube.
Radiation is heat transfer by electromagnetic waves and does not require contact.
Transmission is a general term, not a technical mode of heat transfer.
So, conduction is the correct answer for heat flow through metal.