Step 1: The reaction with \(\mathrm{Br_2}\) in \(\mathrm{CCl_4}\) adds bromine across the double bond of propene (\(\mathrm{C_3H_6}\)), forming a vicinal dibromide (X).
Step 2: Treatment with alcoholic KOH causes dehydrohalogenation, forming an alkyne (Y).
Step 3: Reaction with sodium amide (\(\mathrm{NaNH_2}\)) ensures formation of the alkyne, which on hydration with \(\mathrm{Hg^{2+}}\), \(\mathrm{H^+}\) (acidic medium) undergoes keto-enol tautomerism forming the ketone acetone (Z). Thus, Z is acetone.