You want to display categories and/or subcategories on archive pages? the shop page? the categories and tags pages?

You can do that via the Theme Customizer.

1- To open the theme customizer, go to your admin dashboard -> Appearance -> Customize

Theme Customizer


2- A list of all the theme customizer options will appear, navigate to WooCommerce -> Product Catalog

You have 2 main options:
1- SHOP PAGE DISPLAY: as it sounds, this option affects the shop page and you can choose what to display, categories only or products only or both.
2- CATEGORY DISPLAY: this option affects product categories. You have 3 options, show products only, subcategories only or both.
What to display on archive pages.

What to display on archive pages.