The Fe_3Fe3 in Fe_3O_4Fe3O4 on the right implies that there must be some multiple of 33 FeFe on the left side.
Similarly the O_4O4 on the right side implies that there must be some multiple of 44 H_2OH2O on the left side.
(3m)Fe+(4n)H_2O = (p)Fe_3O_4+(q)H_2(3m)Fe+(4n)H2O=(p)Fe3O4+(q)H2
Since
color(white)("XXX")(3m)Fe rarr (m)Fe_3O_4XXX(3m)Fe→(m)Fe3O4 (there's no place else for the FeFe to go)
and
color(white)("XXX")(4n)H_2O rarr (n)Fe_3O_4XXX(4n)H2O→(n)Fe3O4 (there's no place else for the OO to go)
rArr m=n⇒m=n
Further
color(white)("XXX")(4n)H_2O rarr (q)H_2XXX(4n)H2O→(q)H2
rArr q=4n⇒q=4n
Therefore we have
color(white)("XXX")(3n)Fe+(4n)H_2O = (n)Fe_3O_4+(4n)H_2XXX(3n)Fe+(4n)H2O=(n)Fe3O4+(4n)H2
Using the simplest version: n=1n=1 gives
color(white)("XXX")3Fe+4H_2O = Fe_3O_4+4H_2XXX3Fe+4H2O=Fe3O4+4H2