AE=2。 Connect Me, MF and EF, and make BC vertical line from E and eg; Because point M is folded from point D, so DE=EM, let AE=x, then EM=DE= 12-x, GM=BC-BC-CM=8-x, GE = AB = 8；; According to Pythagorean theorem, GE square +GM square =EM square and x=2.