"Gogy Style" is a slang term for alcohol-induced erectile dysfunction. This condition is characterized by difficulty achieving and/or maintaining an erection after drinking.
The person afflicted by this usually resorts to then licking his partner all over their face body.
How did it go last night with Emma?
Oh man I drank way too much and did it Gogy style with her. Couldn't get it up so I licked her all over