(i)
(a) When methyl bromide is treated with sodium metal in presence of dry ether, coupling takes place to give ethane. Reaction is known as Wurtz's reaction and also called as coupling reaction of alkyl halide.
$$C{H}_{3}Br \xrightarrow{Na, ether} C{H}_{3}-C{H}_{3}$$
Thus, $$X$$ is $$C{H}_{3}C{H}_{3}$$.
(b)The reaction of ethane with bromine called a substitution reaction.
$$C{H}_{3}-C{H}_{3} \xrightarrow[h \nu]{{Br}_{2}} C{H}_{3}C{H}_{2}Br$$
Thus, $$Y$$ is $$C{H}_{3}C{H}_{2}Br$$.
(c) Next reaction is also Wurtz's reaction and will form butane.
$$C{H}_{3}C{H}_{2}Br \xrightarrow{Na, ether} C{H}_{3}-C{H}_{2}-C{H}_{2}-C{H}_{3}$$
Thus, $$Z$$ is $$C{H}_{3}C{H}_{2}C{H}_{2}C{H}_{3}$$.
(ii)
(a) When $$NaOH$$ added to acetic acid, t hey react to form sodium acetate and water. This is a typical acid + base neutralization reaction.
$$C{H}_{3}COOH \xrightarrow{NaOH} C{H}_{3}COONa + {H}_{2}O$$
Thus, $$X$$ is $$C{H}_{3}COONa$$.
(b) When sodium acetate is treated with soda lime, decarboxylation takes place and $$CO_2$$ is eliminated from the sodium acetate.
$$C{H}_{3}COONa \xrightarrow[CaO]{NaOH} C{H}_{4} + {Na}_{2}C{O}_{3}$$
Thus, $$Y$$ is $$C{H}_{4}$$.
(c) This reaction between methane and bromine happens in the presence of ultraviolet light - typically sunlight. This is a good example of a photochemical reaction.
$$C{H}_{4} \xrightarrow[h \nu]{{Br}_{2}} C{H}_{3}Br + HBr$$
Thus, $$Z$$ is $$C{H}_{3}Br$$