The standard heat of reaction is -178.3 kJ.
We have the following information:
For most chemistry problems involving #ΔH_f^"o"#, you need the following equation:
#ΔH_(rxn)^"o" = ΣΔH_f^"o"("p") - ΣΔH_f^"o"("r")#,
where #"p"# = products and #"r"# = reactants.
#ΣΔH_f^"o"("p") = 1 cancel("mol CaCO₃") × "-1206.9 kJ"/(1 cancel("mol CaCO₃")) = "-1206.9 kJ"#
#ΣΔH_f^"o"("r") = 1 cancel("mol CaO") × "-635.09 kJ"/(1cancel("mol CaO")) + "1 mol" cancel("CO₂") × "-393.509 kJ"/(1cancel("mol CO₂")) = "-1028.599 kJ"#
#ΔH_("rxn")^"o" = ΣΔH_f^"o"("p") - ΣΔH_f^"o"("r") = "-1206.9 kJ + 1028.599 kJ" = "-178.3 kJ"#