$n_{Fe_3O_4}=\dfrac{2,32}{232}=0,01(mol)$
$3Fe+2O_2\buildrel{{t^o}}\over\to Fe_3O_4$
$\Rightarrow n_{O_2}=0,01.2=0,02(mol)$
$2KMnO_4\buildrel{{t^o}}\over\to K_2MnO_4+MnO_2+O_2$
$\Rightarrow n_{KMnO_4}=0,02.2=0,04(mol)$
$\to m_{KMnO_4}=0,04.158=6,32g$