To solve this problem using Hess's Law, we need to manipulate the given reactions and their enthalpy changes to match the desired reaction. The desired reaction is:2 CH4 + 4 O2 2 CO2 + 4 H2OFirst, we need to break down the methane CH4 into its constituent elements:CH4 C + 2 H2However, we don't have the enthalpy change for this reaction. We can obtain it by manipulating the given reactions.We can start by reversing the reaction H2:CO2 C + O2 H = +394 kJ/mol Next, we need to multiply the reaction H3 by 2 to get 2 moles of H2O:2 H2 + 1/2 O2 H2O H = 2 * -286 kJ/mol = -572 kJ/mol Now, we can add the reversed H2 and the multiplied H3:CO2 C + O2 H = +394 kJ/mol 2 H2 + 1/2 O2 H2O H = -572 kJ/mol -----------------------------------------------C + 2 H2 + O2 CO2 + 2 H2O H = -178 kJ/mol This reaction represents the breakdown of methane into its constituent elements and their subsequent reaction with oxygen to form CO2 and H2O. Now, we can multiply this reaction by 2 to match the desired reaction:2 C + 2 H2 + O2 CO2 + 2 H2O H = 2 * -178 kJ/mol = -356 kJ/mol Finally, we have the enthalpy change for the desired reaction:2 CH4 + 4 O2 2 CO2 + 4 H2O H = -356 kJ/mol