The Lewis structures in which there are no formal charges is the most stable. Hence, structure (b) is the more stable form of FNO2.
Lewis structure
The question is incomplete but I will try to answer you as much as I can. Now the equation is missing hence we can't numerically caculate the enthalpy chnage of the reaction from bond energies. However, we can do this using the formula; Σbond energy of reactants - bond energy of products.
Concerning the Lewis structures of FNO2, the most stable structure is structure (b) as shown in the image attached where the atoms have no formal charges.
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