Given (A) 2CO(g) + O _ 2 (g) → 2 CO _ 2 (g) Δ H _ 1 ^ o = - xkJ mol...

(A) $2CO\left(g\right) + {O}_{2}\left(g\right) \to 2{CO}_{2}\left(g\right){\Delta H}_{1}^{o} = - xkJ{mol}^{- 1}$

(B) ${C}_{graphite} + {O}_{2}\left(g\right) \to {CO}_{2}\left(g\right){\Delta H}_{2}^{o} = - ykJ{mol}^{- 1}$

If the equation is multiplied the value $n$, then the enthalpy change value also multiplied by factor $n .$ If the enthalpy is positive in one direction, it is negative in other direction.

Multiply equation $B$ by $2$ and subtract equation $\left(A\right)$ from it

$2{C}_{graphite} + {O}_{2}\left(g\right) \to 2CO\left(g\right){\Delta H}^{∘} = x - 2y$

${C}_{graphite} + \dfrac{1}{2}{O}_{2} \to CO; {\Delta H}^{∘} = \dfrac{x - 2y}{2}$