According to the image, the atomic mass of carbon is 12.011. how is the atomic mass of carbon, or any other element, determined?

We don't have the image, but we can still answer the question.

An atom is comprised of 3 major particles: neutrons, protons and electrons.  The neutrons and protons are in the nucleus of the atom, while the electrons are doing orbits around the nucleus.

Most of the mass of an atom is in its nucleus, counting only neutrons and protons.

We add up the number of protons and neutrons located in the nucleus (6 and 6 for carbon) as we have the Atomic Mass Unit (A.M.U.) of the atom. Neutrons are slightly heavier than protons, while electrons have a relatively negligible weight.