PNP or NPN Transistor for this schematic?
That quote is just wrong.

That circuit is correct, but not for your application as it will require about 8V minimum input to give 6V at the output.

It works by supplementing the output current of the 78xx (7806 for 6V) regulator if the regulator takes significant current (about 600mA) with additional current through the PNP transistor.

Your Lipo batteries will not have a constant output voltage, they will probably vary between 8.4V when fully charged down to about 6V or even less when discharged.

What do you need the 6V for? How much current do you need?  What is the acceptable voltage range for the load?