You know that the equation for the formation of ethanol from its elements is:
2 C + 3 H2 + 1/2 O2 --> C2H5OH.
This is the equation that you want to find the enthalpy change for. You have been given several equations that you will need to manipulate so that when you add them all together, you get the equation you are looking for. You've been given these:
C + O2 --> CO2 DH = -393 kJ/mol
H2 + 1/2 O2 --> H2O DH = -286 kJ/mol
C2H5OH + 3 O2 --> 2 CO2 + 3 H2O DH = -1368 kJ/mol
Remember that if you double an equation, you multiply its DH by 2. If you reverse an equation, you change the sign of its DH.
So, take the first equation and multiply it by 2:
2 C + 2 O2 --> 2 CO2 DH = -786 kJ
Take the next one and multiply it by 3:
3 H2 + 3/2 O2 --> 3 H2O DH = -858 kJ/mol
Finally, flip the third equation over:
2 CO2 + 3 H2O --> C2H5OH + 3 O2 DH = +1368
When you add these three equations ( and their DH values), you have:
2 C + 1/2 O2 + 3 H2 --> C2H5OH DH = -276 kJ/mol