what is the answer to this

Except for the diagonal piece we just have to count squares along the perimeter. Let's focus on the diagonal.
It's the diagonal of right triangle that's 6 wide and 8 tall, so the diagonal is 10, (6,8,10) being twice (3,4,5), the first Pythagorean triple on the list.
d² = 6² + 8² = 10²
d = 10
The rest is counting. We already know the height is 8. The top is 8 too, the bottom is 8 plus the 6 we already counted, so 14.
P = 8 + 8 + 14 + 10 = 40
Answer: 40