Consider that the crescent shaped semi-circles are full circles, with adjacent shapes subtracted in the desired order to create the objective.
Create one circle, then a polar array at 90° rotation for three additional copies. It will be necessary to perform progressive subtraction/difference in an appropriate order for each adjacent circle, which will give you the primary shape.
Create a final circle in the center of the array and subtract that from the total array.
I've couched the solution in general terms, as the task can be accomplished in many different graphics programs, but the specific menu selections and commands will be phrased differently from one to another.
Update: after posting the above recommendation, I discovered a slightly easier method. Create one circle, copy it to the first 90° rotation location and perform the difference/subtraction. The result will be the half-moon shape desired. Keeping the same center of polar rotation, create the three other copies.
I found it easier to use the bitmap from a screen cap of your image as a reference. There are some inaccuracies in the image, but nothing a minor adjustment to the vectors didn't solve. It was also easier to create the center circle and use its center as the polar rotation point, but not include it in the subtraction action until the last sequence.