63. (nh₄)₂co₃\na. soluble\nb. insoluble\n64. caso₄\na. soluble\nb. insoluble\n65. bano₃\na. soluble\nb…

Explanation:

Step1: Recall solubility rules

Salts of ammonium ($NH_4^+$) are soluble. So, $(NH_4)_2CO_3$ is soluble.

Step2: Recall sulfate solubility

Most sulfates are soluble, but calcium sulfate ($CaSO_4$) is slightly soluble and often considered insoluble in general - solubility - based questions.

Step3: Recall nitrate solubility

All nitrates ($NO_3^-$) are soluble. So, $Ba(NO_3)_2$ (assuming it's $Ba(NO_3)_2$ as $BaNO_3$ is not a correct formula) is soluble.

Step4: Recall hydroxide solubility

Most hydroxides are insoluble, and iron - (III) hydroxide ($Fe(OH)_3$) is insoluble.

Step5: Recall chloride solubility

Most chlorides are soluble, but silver chloride ($AgCl$) is insoluble.

Step6: Recall phosphate solubility

Most phosphates are insoluble, and magnesium phosphate ($Mg_3(PO_4)_2$ - assuming it's the correct formula as $MgPO_4$ is not a correct formula) is insoluble.

Answer:

63. a. soluble
64. b. insoluble
65. a. soluble
66. b. insoluble
67. b. insoluble
68. b. insoluble