The answer is 64cm (perimeter). However, I do not understand the additional 8cm (4×2) of the perimeter. In my understanding, the perimeter is derived from the outer part of the figure. Could you explain more on this part?

U hv to include the 4 sides of the center square (unshaded), which is belong to the figure too

This is a well designed question. A lot students missed out the centre part

Perimeter is the profile cover all edges of the figure, does NOT mean only refer to the outer parts

Thanks for your valuable comments.