Steps to solve the question:
(1) find the number of moles of HCl and Ba(OH)2 in the mixture
(you should find that these numbers are the same)
(2) find the number of moles of H+ and OH- ions (by mole ratio)
(3) given the enthalpy change for neutralization, multiply this value with the number of moles of H2O to be formed to find the total amount of energy released
(4) since you know the specific heat capacity of water, you can work out the temperature change by the equation Q = mcT (the trick is: what is the volume of the mixture? 200ml or 400ml?)
Don't get confused by the various molarities of HCl and Ba(OH)2 solutions. Always convert concentrations to numbers of moles before doing any calculations. Mole is the most basic and most convenient units in this type of calculations.
