Williamson synthesis involves the reaction of an alkyl halide with a sodium alkoxide to form an ether, which proceeds via a nucleophilic substitution (SN2) mechanism. Thus, A matches with III.
Friedel-Crafts reaction involves the alkylation or acylation of an aromatic ring in the presence of a Lewis acid catalyst, which proceeds via an electrophilic substitution mechanism. Thus, B matches with IV.
Bromination of vinyl benzene (styrene) involves the addition of bromine across the carbon-carbon double bond, which proceeds via an electrophilic addition mechanism. Thus, C matches with I.
Chlorination of toluene in the presence of sunlight (or UV light) involves the substitution of hydrogen atoms in the methyl group by chlorine, which proceeds via a free radical substitution mechanism. Thus, D matches with II.
The correct matching is A-III, B-IV, C-I, D-II.
Answer: A-III, B-IV, C-I, D-II