Not sure how much I can help but there are some mistakes worth (IMO) mentioning.
Two excited nuclear energy levels (of Pt-125) are given as 0.1298MeV (=129.8keV) and 0.0989MeV (=98.9keV). Note that the difference between these is 0.0309MeV (= 30.9keV).
But there are then various references (including in the model-answer) to ‘0.1298keV’, ‘0.0989keV’ and ‘0.0309keV’. It appears that units are very messed up.
Also, the model-answer refers to an ‘energy level of 0.0309keV’. Even after correcting the unit, this value is not an energy level; it is the transition energy between the two excited nuclear states. (What the model answer is telling you is that for each electron-capture, there are two possible nuclear emissions: a ##\gamma## photon of energy 30.9keV or one of 98.9keV. Note that only one of these is in the energy-range of interest.
I’m not familiar with some of the symbols used (despite several years of being a medical physicist in radiotherapy a long time). But I would suggest that you check the energies of characteristic X-rays for Pt-125 to see which ones are in the energy range of interest.
Edit: minor changes only.