A 7812 is a 12v output regulator, not a 6v output. 7806 regulators are not as common as 7805's (Radio Shack 276-1771). But you can stick 2 forward biased diodes (1N4001) in series from the common terminal to ground and get ~6.2V out from the 7805. Don't forget to add two 0.1µF capacitors between the input and common, and the output and common to prevent oscillation.
Ken