Amphoterism is the principle that a strong base will make a weak base act as an acid by giving up a proton. (An acid is a proton donor).
The Aluminum Subgroup Hydroxides are amphoteric and therefore dissolve in excess base (NaOH).
acid + base ----> a salt + water
The salts are soluble and are therefore separated from the Nickel group precipitates which are not amphoteric.
So in Procedure 16, NaOH is added to dissolve the Aluminum Subgroup.
There is nothing unusual about these reactions. Basic hydroxides of metals react with acids to form salts and water. A hydroxide that has the property of reacting with either a strong acid or a strong base is said to be amphoteric.
The hydroxides of aluminum, chromium, tin, lead, and antimony are amphoteric. They react with strong acids in the manner typical of the basic hydroxides of metals.