So first you have to form an equation for the combustion of ethane:
2(C2H6) + 7(O2) = 4(CO2) + 6(H2O)
Then you have to break all the bonds in ethane and oxygen:
12 x C-H (which requires 12 x 413 kJ mol-1)
2 x C-C (which requires 2 x 348 kJ mol-1)
7 x O=O (which requires 7 x 498 kJ mol-1)
which requires in total (12x413)+(2x348)+(7x498)= 9138 kJmol-1
so you have used up 9138 kJ mol-1
Now you have to work out how much energy is released when bonds are made making CO2 + H2O:
O=C=O H-O-H
8 x C=O (8 x 748)
12 x O-H (12 x 468)
so in total, making bonds has released 11600 kJmol-1
so 11600-9138= 2462 kJ mol-1
So 2462 kJ mol-1 has been released, so the reaction is exothermic, so the enthalpy of combustion is negative-
so (delta)HC = -2462 kJ mol-1
Hope this helps. You should draw a Hess' law diagram on your paper- it will make it easier to calculate and will allow the examiner to see that you have calculated it correctly.
Good luck!!