While researching life during colonial times, carson learns that people would extract potassium hydroxide from wood ashes and mix it with animal fat. what were the colonists doing

The colonists were making soap. A lot of people don't know that soap is the result of reacting a base (potassium hydroxide) and an acid (animal fat) which produces a salt which is the white stuff we see in soap. This process is called saponification. Manufacturers just put additives like colors and scents to make them more appealing.

Yup no bull frogs here man