Solution

In (a) , due to the presence of (4n+2) $$\pi e^-$$ it follows Huckel's rule and therefore, it is aromatic.

In (b) , due to the presence of extra lone pair of electrons , total $$e^-$$ comes out to be $$4n$$ $$ \pi e ^-$$.Thus , it is anti-aromatic.

In (c) , although it is cyclic and has conjugated $$8\pi e^-$$ but Huckel's$$(4n+2)\pi$$ rule is not followed and also ring is not planar. Hence, it is non-aromatic.

In (d) , it has $$6\pi e^-$$ in conjugation but not in the ring , hence it is non-aromatic.