Explain how heat transfer is occurring through convection, radiation and conduction in this picture.

Heat is type of energy can be transferred in three different ways:

1) direction contact through collisions (also called conduction).  

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 (in this example hot liquid) to a colder body (in this example spoon).

2) through a fluid making a current created by less dense fluids floating and more dense fluids sinking (also called convection).  

Stirring hot liquid with spoon.

3) by waves traveling with or without a medium (also called radiation).

Waves radiate from hot liquid.

a corroding iron, if that's one of your choices