Anti-aromatic follows the 4n rule. So if you have a cyclic conjugated ring, it will either by anti aromatic or aromatic depending on the number of pi electrons. So if you had benzene thats 6 pi electrons so you use huckels rule 4n+2 = 6 solve for n and u get 1 which is a whole number so benzene is aromatic. If you have a cyclic conjugated ring with lets say 8 pi electrons then try to set it equal to 4n+2. So 4n+2 = 8 where n equals 6/4 which is not a whole number. So its not aromatic. So try the anti-aromatic equation 4n. 4n=8 where n equals 2. 2 is a whole number so a conjugated cyclic ring with 8 pi electrons will be anti-aromatic. Non aromaticity refers to something that doesnt have conjugated double bonds or isnt a ring. so hexene or cyclohexene are non-aromatics.