Final answer:
The structure with a nitrogen-nitrogen bond order of 2 is dinitrogen tetraoxide (N₂O₄), which has a double bond between nitrogen atoms in one of its resonance forms.
Step-by-step explanation:
Among the given structures, the ones with a nitrogen-nitrogen bond order of 2 are those that contain a double bond between two nitrogen atoms. A bond order of 2 indicates a double bond. From the descriptions provided, the structure containing the -N=C=O fragment doesn't have a nitrogen-nitrogen bond, thus it can't have a nitrogen-nitrogen bond order of 2.
The Lewis structures described do not provide clear evidence of a nitrogen-nitrogen bond order; they seem to be describing the ammonia molecule (NH3), which only contains single bonds. On the other hand, the structure mentioned as dinitrogen tetraoxide (N₂O₄) is a likely candidate as dinitrogen tetroxide typically has a nitrogen-nitrogen bond that can be represented as a double bond, especially in one of its resonance forms.
Therefore, the structure with a nitrogen-nitrogen bond order of 2, based on the information provided, would be dinitrogen tetraoxide (N₂O₄).