Write the balanced chemical reaction (showing appropriate symbols and states) for the chemical reaction with enthalpy change equal to and defined by the quantity dHformation [NH3(g)]

N2(g) + 3H2(g) --> 2NH3(g)

Is that all the question is asking for?

No but I'm having a little trouble understanding the problem. Look up the dHo formation for NH3. I'll call that x. IF THE problem is asking for dH rxn it is

N2(g) + 3H2(g) ==> 2NH3(g) + 2x kJ

BUT IF THE problem wants dHo formation for NH3/mol it is
1/2 N2(g) + 3/2 H2(g) ==> NH3 + x

That "equal to and defined by the quantity" makes me think it is the latter but I'll leave it to you to decipher.

Yes, that is the correct balanced chemical reaction for the formation of ammonia (NH3) from nitrogen gas (N2) and hydrogen gas (H2). The reaction shows that one molecule of nitrogen gas reacts with three molecules of hydrogen gas to form two molecules of ammonia, with the enthalpy change defined by the quantity ∆Hformation [NH3(g)]. The reaction equation is correctly balanced, indicating that the number of each type of atom on both sides of the equation is the same. The state symbols (g) indicate that all the reactants and products are in the gaseous state.