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"_4#
Note that the iron is present in two different oxidation states.
Also, the #("NH"_4)_2"Fe"("SO"_4)_2# is just a double salt of #("NH"_4)_2"SO"_4#and #"FeSO"_4#.
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.
