Exothermic reactions:
1) release heat to the surroundings
2) the change of enthalpy, ΔH, is negative: ΔH < 0
3) the temperature of the system increases
With that you can conclude about every equation given:
NH3(g) + 12.0 kcal → ½N2(g) + 3/2 H2(g) : is not exothermic because heat in the side of the reactants means that heat is being used, not released.
C(graphite) → C(diamond), ΔH = - 0.45 kcal : is exothermic because ΔH is negative
C + 2S → CS2, ΔH = 27,550 cal: is not exothermic because ΔH is positive
CH4 + 2O2 → CO2 + 2H2O + 212,800 cal : is exothermic because heat appears as a product of the reaction, which means that it is released.
2H2O → 2H2 + O2, ΔH = +58 kcal : is not exothermic because ΔH is positive.