Answer
$w=0$
$\Delta U=-553.8\,kJ/mol$
Work Step by Step
$\Delta n=\text{number of moles of product gas}-\text{number of moles of reactant gases}$
$=6-(3+3)=0$
$w=-\Delta(nRT)=RT(0)=0$
$\Delta U= \Delta H-\Delta(nRT)$
$=\Delta H-RT\Delta n=\Delta H-RT(0)=\Delta H$
As we multiplied the given equation by 3,
$\Delta U=\Delta H=3\times-184.6\,kJ/mol=-553.8\,kJ/mol$