Given,

$${C_{(diamond)}}\buildrel {} \over \longrightarrow {C_{(graphite)}} + X\,kJ\,mo{l^{ - 1}}$$ ............ (1)

$${C_{(diamond)}} + {O_2}(g)\buildrel {} \over \longrightarrow C{O_2}(g) + Y\,kJ\,mo{l^{ - 1}}$$ ............. (2)

$${C_{(graphite)}} + {O_2}(g)\buildrel {} \over \longrightarrow C{O_2}(g) + Z\,kJ\,mo{l^{ - 1}}$$ .............. (3)

Condition for temperature : constant

Hess's law is applied here. (Hess's law of constant heat summation)

The given reactions (2) and (3),

(2) - (3) $\Rightarrow$

$${C_{(diamond)}} + {O_2}(g) - \left( {{C_{(graphite)}} + {O_2}(g)} \right)\buildrel {} \over \longrightarrow C{O_2}(g) + Y - \left( {C{O_2}(g) + Z} \right)$$

$${C_{(diamond)}} + {O_2}(g) - {C_{(grpahite)}} - {O_2}(g)\buildrel {} \over \longrightarrow C{O_2}(g) + Y - C{O_2}(g) - Z$$

$${C_{(diamond)}} - {C_{(graphite)}} \to Y - Z$$

$${C_{(diamond)}} \to {C_{(graphite)}} + (Y - Z)$$ ............. (4)

Comparing (1) and (4),

$$X = Y - Z$$

So, the correct answer is option (2) $$X = Y - Z$$