For the process :

$\mathrm{X}\left(g\right)+e^{-}\to \mathrm{X}-\left(g\right),\mathrm{\Delta H}=-x$

$\text{ and }\mathrm{X}-\left(g\right)\to \mathrm{X}\left(g\right)+e^{-},\mathrm{\Delta H}=+y$

Select correct alternate :

The correct statements are,

$\text{ ionisation energy of }{\mathrm{X}}^{-}\left(\mathrm{g}\right)\text{ is }y$

$\text{ electron affinity of }\mathrm{X}\left(\mathrm{g}\right)\text{ is }x$

$\text{ electron affinity of }\mathrm{X}\left(\mathrm{g}\right)\text{ is }y$

The ionization energy of the reaction is equal to the change in the enthalpy when the electron is released from any reaction. While the electron affinity is equal to the change in enthalpy when the electron is added in any reaction.
Hence,

Ionization Enthalpy is always positive. Ionization enthalpy is the minimum amount of energy which is required to knock out the most loosely bound electron from an isolated gaseous atom to convert it into a gaseous cation. Whereas ionization energy is the amount of energy required to remove the electron from ground state to infinity.

Therefore, option D is correct.