Understand that an exothermic process is one that releases heat to the surroundings, meaning the enthalpy change (\$\(\Delta\) H\$) is negative.
Analyze each given chemical equation and recall or look up whether the reaction is known to release or absorb heat.
For the decomposition of calcium carbonate (\$\(\mathrm{CaCO_3(s) \rightarrow CaO(s) + CO_2(g)}\)\$), recognize this is a thermal decomposition that requires heat input, so it is endothermic (absorbs heat).
For the formation of nitric oxide (\$\(\mathrm{N_2(g) + O_2(g) \rightarrow 2NO(g)}\)\$), note that this reaction requires high energy input (like a spark), so it is endothermic.
For the formation of liquid water from hydrogen and oxygen gases (\$\(\mathrm{2H_2(g) + O_2(g) \rightarrow 2H_2O(l)}\)\$), this is a combustion reaction that releases a significant amount of heat, making it exothermic.