The balanced equation is
3("NH"_4)_2stackrelcolor(blue)("+2")("Fe")("SO"_4)_2 + 2"K"_3 stackrelcolor(blue)("+3")("Fe")"(CN)"_6 → stackrelcolor(blue)("+2")("Fe"_3)[stackrelcolor(blue)("+3")("Fe")"(CN)"_6]_2 + 3("NH"_4)_2"SO"_4 + "3K"_2"SO"_43(NH4)2+2Fe(SO4)2+2K3+3Fe(CN)6→+2Fe3[+3Fe(CN)6]2+3(NH4)2SO4+3K2SO4
Note that the iron is present in two different oxidation states.
Also, the ("NH"_4)_2"Fe"("SO"_4)_2(NH4)2Fe(SO4)2 is just a double salt of ("NH"_4)_2"SO"_4(NH4)2SO4and "FeSO"_4FeSO4.
The ammonium sulfate doesn't take part in the reaction, so we can rewrite the equation as
underbrace(3stackrelcolor(blue)("+2")(color(red)("Fe"))"SO"_4)_color(red)("iron(II) sulfate") + underbrace(2color(blue)("K")_3 stackrelcolor(blue)("+3")("Fe""(CN)"_6))_color(red)("potassium hexacyanoferrate(III)") → underbrace(stackrelcolor(blue)("+2")(color(red)("Fe"))_3[stackrelcolor(blue)("+3")("Fe")"(CN)"_6]_2)_color(red)("iron(II) hexacyanoferrate(III)") + underbrace(3color(blue)("K")_2"SO"_4)_color(red)("potassium sulfate")
We see that the "K"^"+" and "Fe"^"2+" ions have changed partners.
This is the classic definition of a double decomposition reaction.
