We can work this out using the formula for the circumference of a circle, $c=\pi d$. We can see the diameter of the circle is 4cm, the same as the length of the shortest edge of the rectangle. The circumference of a circle with a diameter of 4cm would be 4$\pi$. However we only have half a circumference here, so the length of the curved edge is 2$\pi$. This means the total perimeter of the shape is:
$6+4+6+2\pi =22.3$ (1 d.p.)