$n_{Fe}=\dfrac{8,4}{56}=0,15 mol$
$Fe_xO_y+yH_2\buildrel{{t^o}}\over\to xFe+yH_2O$
$\Rightarrow n_{Fe_xO_y}=\dfrac{0,15}{x}$
$M_{Fe_xO_y}=\dfrac{11,6x}{0,15}=\dfrac{232x}{3}=56x+16y$
$\Leftrightarrow \dfrac{x}{y}=\dfrac{3}{4}$
$\Rightarrow x=3; y=4(Fe_3O_4)$
$n_{H_2}=\dfrac{0,15y}{x}=0,2 mol$
$\Rightarrow V_{H_2}=0,2.22,4=4,48l$