The common method used to prepare ethane is X, while ethene and ethyne is Y. Now, X and Y respectively are

 The process of dehydrogenation involves removing hydrogen from an organic substance to create a new chemical.

In Kolbe's electrolysis process, the equivalent alkane is produced using the sodium salt of the fatty acid.

The sodium salt of the fatty acid undergoes decarboxylation in this process.

$\mathrm{HC}\equiv \mathrm{CH}$ Or ${\mathrm{H}}_2\mathrm{C}={\mathrm{CH}}_2\left(\mathrm{Y}\right)⟶$ Dehydrogenation

${\mathrm{H}}_3\mathrm{C}-{\mathrm{CH}}_3\left(\mathrm{X}\right)⟶$ Kolbe's Electrolysis

Hence the correct option is (C).