Hard to say without seeing the code in the Theme.
The ways I see this done include:
- manually, or using a page editing app to build the layout
- Setting the sub collections in a metafield. Theme code grabs the collections listed in the metafields and shows them
- Collection handle matching. So using a known handle/name format so. Code loops over all collections it can and tries to find a match.
If you’re open to sharing some code snippets we might be able to help narrow it down to spark that memory.