How would I go about making an auto suggest/complete with a hierarchy of categories like Etsy does?

My goal is to make something like this, where there are categories and subcategories. How would I do a hierarchy that would include doing things? How would I store/reference the categories and how would I display them to the user? Using jQuery autocomplete? Here is a really good example of something I saw:
https://i.stack.imgur.com/1tA8y.png
A desired result would be something like this:

      Landscaping           Construction
      |         |            |         |
     Mowing    Raking     Roofing    Flooring