The radius of each disc in the figure is equal to half of the side-length of the square, i.e. $1/\pi$.
Because the corners of a square are right-angled, the square hides exactly one quarter of each disc. So
three-quarters of the perimeter of each disc lies on the perimeter of the figure. Therefore the length of the perimeter is $$4\times\frac{3}{4}\times 2\pi\times\frac{1}{\pi}=6\;.$$