As an auxiliary line: extend BC to M to make am parallel to BD, because AC is perpendicular to BD, so AC is perpendicular to AM, and because it is isosceles trapezoid, so AC is equal to BD, because AD is parallel to BC and BD is parallel to AM, so AMBD is a parallelogram, so AM is equal to AC, and because AM is perpendicular to AC, so the triangle AMC is an isosceles right triangle, because AE is perpendicular to CB. So the triangle AEM is an isosceles right triangle, because AD=BM and AE=ME=6, AE+EF=ME+AD= 10.