(A) The $IUPAC$ nomenclature rules are applied to each structure:
$(i)$ The longest chain has $5$ carbons with a double bond at $C-2$ and a bromine at $C-4$. Name: $4$-Bromopent-$2$-ene.
(ii) The longest chain has $5$ carbons with a double bond at $C-2$,a methyl group at $C-3$,and a bromine at $C-4$. Name: $4$-Bromo-$3$-methylpent-$2$-ene.
(iii) The longest chain has $4$ carbons with a double bond at $C-2$,a methyl group at $C-2$,and a bromine at $C-1$. Name: $1$-Bromo-$2$-methylbut-$2$-ene.
(iv) The longest chain has $5$ carbons with a double bond at $C-2$,a methyl group at $C-2$,and a bromine at $C-1$. Name: $1$-Bromo-$2$-methylpent-$2$-ene.
Therefore,the correct matching is: $(i-a, ii-b, iii-c, iv-d)$.