How do I create multi-category fly-out menus

So I’m building a furniture website and products are categorized by product type and age, like this:

Product Type (Parent Category)
– Sofas (Child Category)
– Chairs (Child Category)
– Desks (Child Category)

Age (Parent Category)
– New (Child Category)
– Antique (Child Category)

So each product gets checked off into both a child category of Product Type and a child category of Age.

I want to create a list of the Product Type Parent Categories in my sidebar so that it looks like this:

PRODUCT TYPES:
Sofas
Chairs
Desks

but when someone hovers over any of the headings (Sofas, Chairs, Desks), a flyout dropdown will then let them select whether they want that product type that is also New or Antique.

so basically it’ll work something like this:
PRODUCT TYPES:
Sofas >>> New / Antique / All
Chairs >>> New / Antique / All
Desks >>> New / Antique / All

I’m a little confused because there’s two separate parent categories. please advise how I go about about doing this. thanks!