Question

The method of heat transfer by which the sun warms the earth is

Answer 1

Conduction and convection both require some kind of material stuff
between the heat source and the object being heated.

Since there's no material stuff in the space between the sun and the
Earth, conduction and convection can't do it, and the only way for the
sun's energy to reach the Earth is by radiation.

Answer 2

Heat from the Earth's core and radiation from the Sun is transferred to the surface of the Earth by conduction. Contact of the atmosphere with these warm surfaces transfers thermal energy, which then heats up the rest of the air through convection.