Is the dissolution reaction of ammonium nitrate enthalpy favored?
a. No, it is not enthalpy favored since the chemical system loses energy.
b. Yes, it is enthalpy favored since the chemical system loses energy.
c. No, it is not enthalpy favored since the chemical system gains energy.
d. Yes, it is enthalpy favored since the chemical system gains energy.
e. No, it is not enthalpy favored since the chemical system neither gains nor loses energy.

From Fundamentals of Chemistry by Brady& Holum "
"For most solid solutes the formation of a solution is an endothermic process. More energy must be expended breaking apart the latice than is recovered when the solute particles become surrounded by the solvent molecules" (increasing the temperature of the solution increases the solubility).
From the CRC Hanbook of Chemistry and Physics
heat of solution of NH4NO3 @ 25c 1 Mole
+6140 Calories.
Compared to HCL of -17,888 (HCL does get hot when diluted).. The opposite sign says the solution of ammonium nitrate will get a little cooler when just disolving the solid.
Enthapy is not favored .
I'd pick c Your solution takes heat from the environment. and gains thermal energy..

Over all the reaction does proceed to form a solution as the net entropy difference out weighs the enthalpy.

good luck.