Haha, a g-stache is a mustache that is thinner than a real mustache. It is usually associated with young (hence the inability to grow full facial hair) white guys.

I'm guessing - the 'g' could be a 'goatee', which is a beard grown on the chin and looks like a goat's beard. yuk! http://menshair.about.com/od/facialhair/ig/Facial-Hair-Styles/goatee.--5Q.htm