Consider the following data :
$$\Delta_f H^\ominus$$ (methane, g) = - X kJ $$mol^{-1}$$
Enthalpy of sublimation of graphite = Y kJ $$mol^{-1}$$
Dissociation enthalpy of $$H_{2}$$ = Zkj $$mol^{-1}$$
The bond enthalpy of C - H bond is given by :

We need to find the C-H bond enthalpy from the given data.

Formation of methane: $$C(s) + 2H_2(g) \to CH_4(g)$$, $$\Delta_f H = -X$$ kJ/mol.

To find C-H bond energy, we break all bonds in reactant atoms and form 4 C-H bonds:

$$C(s) \to C(g)$$: $$\Delta H = Y$$ kJ/mol (sublimation of graphite)

$$2H_2(g) \to 4H(g)$$: $$\Delta H = 2Z$$ kJ/mol

$$C(g) + 4H(g) \to CH_4(g)$$: $$\Delta H = -4 \times E_{C-H}$$

By Hess's law:

$$-X = Y + 2Z - 4E_{C-H}$$

$$4E_{C-H} = Y + 2Z + X$$

$$E_{C-H} = \frac{X + Y + 2Z}{4}$$

The answer is Option 1: $$\frac{X + Y + 2Z}{4}$$.