Sulfuric acid is a strong acid, which means it can dissociate completely when dissolve in water. In other words, the reactant H2SO4 is completely soluble in water, otherwise, it wouldn't be a strong acid.
On other hand, the second reactant Ba(OH)2 is soluble in water because it's a strong base, which are bases that completely dissociate when dissolve in water.
Therefore, sulfuric acid (H2SO4) is soluble in water and the barium hydroxide (Ba(OH)2) is also soluble in water.