Horizontal Header menu sub-categories

Hi,
I am using a theme (https://www.themeporter.com/2006/10/07/zenlike-wordpress-theme/) that I am using here: https://www.thomasmckee.com/nunanestate/. The challenge I’m working on now is with the horizontal menu on the header.php. I’d like it to work like this: https://www.thomasmckee.com/nunanestate1/ so that hovering over the primary category name the sub-categories pop up under the primary ones. Any ideas?

Thanks in advance.