${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}\stackrel{{\mathrm{KMnO}}_4/{\mathrm{H}}^{\oplus }}{\to }\mathrm{X}\underset{{\mathrm{H}}_2{\mathrm{SO}}_4}{\overset{\mathrm{Y}}{\to }}$CH₃COOC₂H₅. 

X and Y respectively are

 Oxidation of primary alcohol by potassium permanganate (KMnO₄) produces carboxylic acid.

${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}\stackrel{{\mathrm{KMnO}}_4/{\mathrm{H}}^{+}}{\to }\underset{ }{\underset{\left(\mathrm{X}\right)}{{\mathrm{CH}}_3\mathrm{COOH}} \underset{{\mathrm{H}}_2{\mathrm{SO}}_4}{\overset{{\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}\left(\mathrm{Y}\right)}{\to }}{\mathrm{CH}}_3{\mathrm{COOC}}_2{\mathrm{H}}_5}$

The sequence of reaction is an oxidation reaction (ethanol to acetic acid) followed by an esterification, where acetic acid and ethanol forms ethyl acetate.

Hence, X is Acetic acid and Y is Ethanol.