Taxonomy block in views which show the description of the children taxonomy, selected by two exposed filters
One way to do this is possible with contextual filters.


Add a contextual filter based on term name
Add a relationship to parent term.
Add another contextual filter on term name, but this time use the parent term from the relationship.
Tweak the settings (override number of items to show, probably remove the count from the item list, and switch to jump menu instead of regular list if you want a dropdown display.)