After arousing your girlfriends sexual interests, you forcibly shove half of your clenched fist up her ass (hence the "quarter", since a "full" would be both fists), whilst simultaneously ejaculating into her anus.
The quarter pounder with cheese:
Bob: Once I got Harriet in the mood, I gave her the ol' "quarter pounder with cheese" to liven things up a little!
Doug: Sick!
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