I only know about Hess' law, bond enthalpies and enthalpies of combustion and have tried to use all concepts in order to somehow get an answer but none of them have worked. I first tried to write a balanced equation for what the reaction of 2 moles of reactants would look like but I don't believe it could be balanced. Then, I tried using bond enthalpies but I couldn't have done that either since the equation couldn't be balanced. Next, I tried using enthalpies of combustion, and the same thing happened. So, I'm wondering if there's anyway to answer this question, preferably with the concepts mentioned above.
The N2O4 is going to define the maximum amount that will be used up in the reaction, since it has the higher stoichiometric number of the reagents. That is, the second term will always be less and the amount consumed will be defined by the N2O4 because that two moles will limit the N2O4 and in doing so reduce the amount of the second term consumed- there will be excess second compound after the N2O4 has been consumed.
For example, the ratio of first to second term is 5:4, so if we consume all of the second term (2 mols) this requires 2.5 mols of N2O4, which we don't have. So we are limited with the N2O4.
So, knowing that, with two mols of N2O4 the amount is reduced to 2/5 of the enthalpic calculation. That becomes 5116*2/5 = 2046, or answer B.
Apologies for awkwardness of this answer, on a mobile device and have to keep swapping from question to answer.