According to the spectrum seen below, which set of photons were absorbed by the element?

You can see that the missing gray bars are at 2ev, 5ev, 8ev, and 15ev, these are the ranges where the photons were not detected (or absorbed by the element)

this is because in this kind of experimets you put the detector behind the element, then the photons that go through it are detected (and not absorbed) and the ones absorbed by the element never reach the detector, and are not detected.

this means that the right answer is D

The red green and blue are (almost) representing the visible spectrum of the energy of the photon, where red is between 1.6ev and 2ev, and violet is between 2.75ev end 3.26ev

c-14 is carbon-14, or radiocarbon.   it is a radioactive isotope of carbon with an atomic nucleus containing 6 protons and 8 neutrons.