If $$C(\text{diamond}) \rightarrow C(\text{graphite}) + X\,\text{kJ mol}^{-1} C(\text{diamond}) + O_2(g) \rightarrow CO_2(g) + Y\,\text{kJ mol}^{-1}C(\text{graphite}) + O_2(g) \rightarrow CO_2(g) + Z\,\text{kJ mol}^{-1}$$ at constant temperature. Then

Given reactions:

1. $$C(\text{diamond}) \to C(\text{graphite}) + X$$ kJ/mol ... (i)

2. $$C(\text{diamond}) + O_2(g) \to CO_2(g) + Y$$ kJ/mol ... (ii)

3. $$C(\text{graphite}) + O_2(g) \to CO_2(g) + Z$$ kJ/mol ... (iii)

By Hess's law, reaction (i) = reaction (ii) - reaction (iii):

$$C(\text{diamond}) \to C(\text{graphite})$$

The enthalpy change for this = enthalpy of (ii) - enthalpy of (iii):

$$X = Y - Z$$

The correct answer is Option 4: X = Y - Z.