Sparty
When you say that you will "install a plug outside" what do you mean?
You can install a cord that is spliced right on to the cable or you can
install a flanged inlet which is the same pins as a plug end of a cord
rigidly fastened to a mount to receive a receptacle cord cap. Do not
install a receptacle at the supply end of the cable.
--
Tom Horne

"This alternating current stuff is just a fad. It is much too dangerous
for general use." Thomas Alva Edison


I would like to run 6 guage wire from my basement to my garage like I
mentioned. I want to make this nice and clean looking. Then on the
outside of my 3rd stall garage, I would like to have something that a
generator can plug into, using an extension cord.

I would like to make about a 10 foot or so 6 guage extension cord. One
side would plug into the generator and the other side to the plug, or
whatever I need to install outside.


Since the generator will be 12000 watts or fifty amperes your least
expensive solution will be to Install a hard wired flexible cord from a
suitably sized junction box at the garage end. That cord will have a
male cord cap that matches the receptacle on your generator. Flanged
inlets in the 240/120 volt fifty ampere pattern are expensive and hard
to find.
--
Tom Horne

Well we aren't no thin blue heroes and yet we aren't no blackguards to.
We're just working men and woman most remarkable like you.