$\begin{array}{c}{\mathrm{S}}_8+8{\mathrm{O}}_2\to 8{\mathrm{SO}}_2 \mathrm{\Delta H}=-\mathrm{XkJ}\\ 1/8{ \mathrm{S}}_8+3/2{\mathrm{O}}_2\to {\mathrm{SO}}_3 \mathrm{\Delta H}=-\mathrm{YkJ}\\ {\mathrm{SO}}_2+1/2{\mathrm{O}}_2\to {\mathrm{SO}}_3 \mathrm{\Delta H}=-\mathrm{ZkJ}\end{array}$

 then,

According to Hess's law, the total change in the amount of enthalpy is the same whether the reaction takes place in one step or a series of steps.

For the given reactions,

$\begin{array}{l}{\mathrm{S}}_8+8{\mathrm{O}}_2\to 8{\mathrm{SO}}_2{\mathrm{\Delta H}}_1=-\mathrm{XkJ}\\ 1/8{ \mathrm{S}}_8+3/2{\mathrm{O}}_2\to {\mathrm{SO}}_3{\mathrm{\Delta H}}_2=-\mathrm{YkJ}\\ {\mathrm{SO}}_2+1/2{\mathrm{O}}_2\to {\mathrm{SO}}_3{\mathrm{\Delta H}}_3=-\mathrm{ZkJ}\end{array}$

On (i) divided by 8 plus(iii), we get,

$\begin{array}{c}1/8{ \mathrm{S}}_8+3/2{\mathrm{O}}_2\to {\mathrm{SO}}_3 ,\mathrm{\Delta H}={\mathrm{\Delta H}}_3+{\mathrm{\Delta H}}_1/8\\ \Rightarrow \mathrm{\Delta H}=-\mathrm{Z}-\mathrm{X}/8\end{array}$

$\Rightarrow \mathrm{\Delta H}=-\left[\mathrm{Z}+\frac{\mathrm{X}}{8}\right]$

Clearly, $\mathrm{\Delta H}={\mathrm{\Delta H}}_2$

Thus, $-\mathrm{Y}=-\left[\mathrm{Z}+\frac{\mathrm{X}}{8}\right]$

Hence, option (C) is correct.