Using the data given, the heat of combustion would be 308 kJ/mol.
To calculate the heat of combustion, you must determine the amount of heat energy released and divide by the number of moles of ethanol combusted.
The heat of combustion is used to raise the temperature of 800 g of water from 23 C to 31 C, or a difference of 8 C. The heat capacity of water is 4.184 J/g/C, so the total heat energy released is
The molar mass of ethanol is 46.07 g/mol. Therefore, the mole of ethanol combusted is
Finally, the heat of combustion of ethanol is calculated to be
HOWEVER! The actual heat of combustion of ethanol is 1370.7 kJ/mol so the data given in the problem are not correct. Most likely, the person who made up the problem forgot to convert from kcal/mol to kJ/mol because the heat of combustion in these units is 328 kcal/mol.