If you look at the six solutions, ammonium chloride is the one that will separate barium ion from lead (II) ion in water.
If you want to separate things in a solution, you can use a solution that preferentially precipitates one of the ions in the solution while leaving the other one in the solution.
Here, we know that chlorides are soluble except those that come from metals like gold and silver because of the rules about which ones can be soluble. This is why, when barium ion and lead (II) chloride are mixed together in water, lead II chloride preferentially precipitates. This means the ions are separated.
I hope this helps you
:)
