Look at Fig. 4.13. Mark where the heat is being transferred by conduction, by convection, and by radiation.
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Heat transfer from the burner to the pan- 

The heat is getting transferred directly from the burner to the pan. it is called conduction of heat when it is transferred by direct contact. So the heat from the burner to the pan is transferred by conduction. In conduction, heat is transferred without the actual movement of molecules.

Heat transfer in boiling of water-

The water inside the pan is boiling. Here, heat is getting transferred by the movement of molecules of fluids. So, it is the convection of heat in boiling water.

Heat transfer from pan, burner plate, etc. to the surrounding-

From the pan, burner plate and boiled water heat waves are getting transferred to the surroundings. This is the radiation of heat. 

Note-

Heat transfers from hot to cold objects, whether this transfer is through conduction, convection, or radiation.

In the picture below, heat transfer is marked where heat is being transferred by conduction, convection, and radiation.