Why can ammonium hydroxide pass through a filter but lead (II) sulfate
cannot?

Lead (II) sulfate is not a liquid.

Explanation:

You'd need a solubility chart for this problem, a chart that can help you determine whether or not a specific compound is a solid or not.

https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Equilibria/Solubilty/Solubility_Rules

Ammonium Hydroxide is a liquid so it can pass through a filter. However, in the rules it states that sulfate salts are soluble except for the exception PbSO4. This is lead sulfate, which means that it is insoluble=solid.

Therefore lead(II) sulfate is not a liquid and cannot pass through a filter.

pie chart because it is in percents ( % )