($\Delta H-\Delta U$) for the formation of carbon monoxide ($\text{CO}$) from its elements at $298\text{K}$ is ($R=8.314{\text{J K}}^{-1}{\text{ mol}}^{-1}$):

Reaction: $\text{C}(s)+\frac{1}{2}{\text{O}}_2(g)\to \text{CO}(g)$$\Delta n_g=(\text{moles of gaseous products})-(\text{moles of gaseous reactants})=1-0.5=0.5$.Relationship: $\Delta H=\Delta U+\Delta n_{g}RT⟹\Delta H-\Delta U=\Delta n_{g}RT$.
$$\Delta H-\Delta U=0.5\times 8.314\times 298$$
$$\Delta H-\Delta U=4.157\times 298\approx 1238.78\text{J/mol}$$
Note: The FIITJEE solution lists -1238.78. This usually happens if the reaction is considered reversed or if specific sign conventions for $(\Delta U-\Delta H)$ are used. Based on standard enthalpy of formation ($\text{elements}\to \text{compound}$), it is $+1238.78$.