Ba(OH)2 (aq) + FeSO4 (aq) --> BaSO4 (s) + Fe (OH)2 (s)
Two soluble solutions reacting to form two insoluble precipitates.
Ferrous hydroxide, Ferric hydroxide and Barium sulfate are insoluble or in other words they are not aqueous.
Ba(OH)2 is soluble and exists as Ba(2+) and 2 OH- ions. Ferrous sulfate reacts with the OH- ion and gives Ferrous hydroxide and a SO4(2-) ion. So if Ba(OH)2 and FeSO4 are mixed, the FeSO4 will react with the OH- ions to give Fe(OH)2, which is insoluble and a SO4(2-) ion that has to be accepted by the Ba(2+) ions resulting in Barium sulfate which is also insoluble.
I am not sure the two chemicals will react but if they do, both the resulting compounds of the reaction will be precipitated.
If a reaction does take place between the two, the balanced equation would be: