Which of the following types of hair removal uses a caustic alkali preparation?

Depilatories are hair removal products that contain caustic alkali agents such as calcium thioglycolate or sodium hydroxide. These agents work by breaking down the hair's structure, making it easy to remove the hair from the skin's surface. The effectiveness of depilatories relies on their chemical composition, which targets the protein structure of hair, leading to its dissolution and removal.

In contrast, waxing involves applying a sticky substance to remove hair from the roots, shaving involves cutting hair at the skin's surface, and threading is a manual method that uses a thin thread to twist around hair strands and pull them out from the roots. None of these methods involve the use of caustic alkali agents for hair removal, which is why depilatories stand out in this context for their specific chemical approach.