How does the approximate number of atoms in the air in your lungs compare to the num-
ber of breaths of air in the atmosphere of the
whole world?

I don’t understand what this is asking...

Consider the Earth as a sphere. Think of the atmosphere as having a height of say about 20000 m. The volume of a sphere is 4/3 * pi * r ^3.
Find the volume of a sphere of radius 6020000 m and subtract the volume of the Earth which is a sphere of radius 6000000 m (approx).
This would be the volume of air in m^3.

Approximate the lungs as a cube, it would be approx 0.2m x 0.2m x 0.2 m = 0.008 m^3

Divide the volume of air around the Earth by 0.008.

0.001 m^3 of air contains about 6 x 10^23 molecules which is about 12 x 10^23 atoms.

If your lungs are 0.008 m^3 then that would be about 96 x 10 ^23 or about 10^25 atoms.

Compare that number with the earlier number when dividing air in the atmosphere by 0.008.

I hope this helps. :)