Points g and f are both moving points, so it is difficult to calculate the maximum value. Rotating point D together with △CEF, it is observed that GF is always the center line of △ADE, so GF is half of AD, the rotation radius of D is the same as that of E, and A is a fixed point, so the maximum value of AD is 6-2√2 and 6+2√2 on the diameter of the connecting line between A and the rotation center.