So 678-862= -184KJ
So, if you calculate the energy needed to break the H-H and the Cl-Cl bond using the data in the table, and subtract the energy released by forming two H-Cl bonds, you'll get the overall energy change.
Exothermic reactions are when energy is released to the surroundings, so the energy released by breaking bonds is greater than the energy used to break them. You can prove this by getting an overall energy change that's negative from this calculation. (: