The difference between electron gain enthalpies will be maximum between:

Electron gain enthalpy (EGE) is the energy change when an electron is added to a neutral gaseous atom.

Noble gases (Ne, Ar) have completely filled electron shells, so they have very positive (highly unfavorable) electron gain enthalpies. They strongly resist gaining an electron.

Halogens (F, Cl) have the most negative (highly favorable) electron gain enthalpies. Among halogens, Cl has the most negative EGE (more negative than F, due to the small size of F causing electron-electron repulsion).

Among noble gases, Ne has a more positive EGE than Ar (smaller size, more repulsion).

Therefore, the maximum difference in electron gain enthalpies would be between the species with the most positive EGE (Ne) and the most negative EGE (Cl).

The correct answer is Ne and Cl.