Imagine the circle and 2 semicircles are stacked on top of one another. When you remove the area of the triangle out, the single layer part on top of the circle will be completely gone. Where as the parts where the circle and semi circles overlap, there are 2 layers hence the layer below will still remain and therefore shaded.

Imagine if the circle and 2 semicircles overlap, the shaded parts are the parts that are overlapped hence 2 layers

When I cut out the triangle, the area in red of the circle is gone and the blue area is left behind.

For the semicircles, the not overlapped parts got cut out as they only have 1 layer (area in red), the shaded area in pencil is still around as it is the top layer of the big circle that has already been cut out.

The blue area is the part where it is not even touched

After cutting, you should be left with these area and when you combine them, you will get the shaded area in the question