Can you help me with my chemistry homework?

I think your last sentence should say "also produce insoluble"?. As there are anions which can produce insoluble by-products with Silver and Barium, - degree of insolubility will be determined by the water make-up, concentration weight of byproduct formed, temperatures and pressures. For example, carbonates can give silver carbonate and barium carbonate. One can find phosphates and oxalate. If you say "soluble" was the condition, then there are no other common ones that those used in your example. Check out the solubilities of silver and barium phosphates, carbonates and oxalates. Thiosulphates and sulphites are less common.