Answer
$\Delta H ^o = -1152.98 kJ$
Work Step by Step
$N_2O_4(g) + 4H_2(g) --> N_2(g) + 4 H_2O(l)$
$\Delta H^o _f : N_2O_4(g) = 9.66 kJ/mol$
$\Delta H^o _f : H_2(g) = 0 kJ/mol$
$\Delta H^o _f : N_2(g) = 0 kJ/mol$
$\Delta H^o _f : H_2O(l) = -285.83 kJ/mol$
$\Delta H^o = (Products) - (Reactants)$
$\Delta H^o = (0 + 4*(-285.83)) - (9.66 + 4*(0))$
$\Delta H^o = -1143.32 - 9.66$
$\Delta H ^o = -1152.98 kJ$