Sorry about my terrible finger writing. But the shape you have has 8 sides that make up its perimeter and you are given 4 of the 8,
But you are also given the length in which the composite figures share that is not apart of the perimeter: 4cm this is useful as subtracting 4cm from two side lengths will reveal the lengths of the unknown sides. Because the composite shape is made of two squares (one with side lengths of 9cm and one with side lengths of 10cm) that share 4cm of contact. I wrote in red and blue to show how I got the two shorter side lengths
Total perimeter: 68cm