The enthalpy change in this case, with no heat lost to the surroundings, the cup itself, and at a constant pressure is equal to the change in energy of the reaction mixture in Joules or Kilojoules per mol.  The formula of choice here is:

q=ms∆t
(Where q is the amount of heat [Equal to Enthalpy], m is the mass, s is the specific heat, and delta T is the change in temperature).

If we solve the equation for the water in the reaction (since the specific heat of water is readily available) we get:

q = (159g)(4.184 J/gºC)(24.7ºC-21ºC)

q = 2461.4472 J = 246 KJ

Now all that remains is to divide the above value by two in order to get the enthalpy change per mol of compound:

2461.4472 J / 2 mol = 1230.7236 J/mol

This is the heat of the reaction. After rounding the above figure to the correct number of significant figures you get your answer.  Just remember that since this is an exothermic reaction that the enthalpy change should be negative.  The only thing lacking here is the mass of the compound you are starting with.  Having this would give a more correct value since it is being mixed with the water so it too is absorbing heat from the environment and gaining in temperature and this mass of compound and the heat that it gains is not reflected in the calculation above, but there is nothing in the problem that could be used to deduce this weight.