The reaction would give off
You are provided with the thermochemical equation that describes the dissociation of sodium hydroxide into its constituent ions when dissolved in water.
#"NaOH"_ ((s)) -> "Na"_ ((aq))^(+) + "OH"_ ((aq))^(-), " " DeltaH_"rxn" = - "46.80 kJ mol"^(-1)#
In this case, the enthalpy change of reaction is essentially the enthalpy change of solution of sodium hydroxide, i.e. the change in enthalpy that occurs when sodium hydroxide is dissolved in water at constant pressure to get an infinite dilution.
The enthalpy change of solution tells you that when
Notice that you have
#DeltaH_"rxn" = - "46.80 kJ mol"^(-1)#
The minus sign is used here to show that heat is being given off.
So, what would happen if you were to dissolve
Since you know that
#4 color(red)(cancel(color(black)("moles NaOH"))) * overbrace("46.80 kJ"/(1color(red)(cancel(color(black)("mole NaOH")))))^(color(blue)(= DeltaH_"rxn")) = "187.2 kJ"#
of heat to be released. This implies that the enthalpy change of reaction when
#DeltaH_"rxn 4 moles" = - "187.2 kJ"#
Once again, we use the minus sign to show that heat is being given off.
So regardless on how many grams of sodium hydroxide you have, you can say that using