Hydrolysis is a chemical reaction where the water molecules are added to the compound undergoing the reaction.
During hydrolysis, the water molecule undergoes decomposition to give \(H^{+}\) and \(O H^{-}\) ions respectively.
\(H O H \rightleftarrows H^{+}+O H^{-}\)
All the given options are examples of metal carbides.
Now, we know that carbides are compounds that have carbon and other elements which have less electronegative character than carbon atoms.
Metal carbides are compounds that have a transition metal ion and carbon atom as the constituents.

These structures are more of a complex type. Propyne is basically, \(C_{3} H_{4}\).
\(M g_{2} C_{3}\) is an ionic carbide and on hydrolysis with water yields magnesium hydroxide and propyne which is a three-carbon product.
\(\mathrm{Mg}_{2} \mathrm{C}_{3}+4 \mathrm{H}_{2} \mathrm{O} \rightarrow 2 \mathrm{Mg}(\mathrm{OH})_{2}+\mathrm{C}_{3} \mathrm{H}_{4}\)
\(A l_{4} C_{3}\) is a metal carbide and on hydrolysis yields methane and aluminium hydroxide.
\(A l_{3} C_{4}+12 H O H \rightarrow 3 C H_{4}+4 A l(O H)_{3}\)
\(B_{4} C\) on hydrolysis gives boron oxide while carbon monoxide and hydrogen gases are evolved.
\(B_{4} C+7 H_{2} O \rightarrow 2 B_{2} O_{3}+C O+7 H_{2}\)
\(L a_{4} C_{3}\) on hydrolysis gives lanthanum hydroxide and methane.
\({La}_{4} {C}_{3}+{HOH} \rightarrow{La}(OH)_{3}+{CH}_{4}\)
Thus, from the above chemical reactions, it is clear that \(M g_{2} C_{3}\) is the correct option. As it gives propyne as a product.