Bromoethane is heated with alcoholic $\mathrm{KCN}$ to give A. A is refluxed with dilute $\mathrm{HCl}$ to complete hydrolysis, giving B. B is

$\mathrm{CH}{}_3\mathrm{CH}{}_2\mathrm{Br}+\mathrm{KCN}\to \mathrm{CH}{}_3\mathrm{CH}{}_2\mathrm{CN}$ adds one carbon, giving propanenitrile (A). Complete acid hydrolysis converts $-\mathrm{CN}$ to $-\mathrm{COOH}$, giving $\mathrm{CH}{}_3\mathrm{CH}{}_2\mathrm{COOH}$ (3 carbons). The amide is only the intermediate stage and the amine needs reduction.