The correct explanation for why the burning of methane gas (as represented by the given chemical equation) is an exothermic process is:
Less energy is absorbed from the breaking of old bonds than is released from the formation of new bonds.
In an exothermic reaction, the energy released when new bonds are formed (in the products) is greater than the energy required to break the old bonds (in the reactants), resulting in a net release of energy, typically in the form of heat.