Maybe off topic given that the following has nothing to do with the wire gauge but.....
If you connect 4.7R to a +12V supply, you will draw 2.55A of current and generate 30.6W of power.
Using a 6V supply, you draw 1.28A and generate 7.6W which is close to what the figures suggest. All I am saying is take care and make sure that you only operate the cartridge when fitted into the hot end heater block and that you have good thermal contact.
Alan