For a compound to be aromatic, it must have $(4 n+2) \pi$ electrons.
Here two double bonds are present, $4 \pi$ electrons are present in the compound. Therefore, it is anti-aromatic.
Homocyclic compounds are ring structures that consist only of carbon atoms within the ring. A nitro group is attached to the ring system as a substituent, so, $C _{6} H _{7} NO _{2}$ is homocyclic but not aromatic.