Which of the following is insoluble in water? ##"NaCl"##; ##"Cu"("OH")_2##; ##"AgNO"_3##; ##"K"_2"SO"_4##

That would be copper (II) hydroxide, or ##Cu(OH)_2##.

You will need to become familiar with the solubility rules, because that will help you determine what are soluble and what compounds are insoluble in water.

Here's what these rules look like

So, start with ##NaCl##, or sodium chloride. The solubility rules tell you that all halides are soluble with the exception of those formed with siver, mercury, and lead ions. Since this is not the case here, sodium chloride will be soluble.

SIlver nitrate, or ##AgNO_3##, is soluble because all nitrates are soluble, without exception. Potassium sulfate, or ##K_2SO_4##, is soluble because all sulfates are soluble with the exception of those formed with silver, calcium, barium, mercury, lead, and strontium ions,

FInally, copper (II) hydroxide, or ##Cu(OH)_2##, is insoluble because all hydroxides are insoluble with the exception of those formed with alkali metal ions and barium.

Here's a link to an interactive version of the solubility rules:

http://periodic-table-of-elements.org//SOLUBILITY