It's going to depend a bit on what you are trying to achieve and how you want the facets to work.
You could have hierarchical facets with a top tier of faculty and second tier of department.
For this you'd need 2 metadata fields - the first one contains the faculty name and the second field contains the department name.
These would then be configured as a hierarchical facet with you first being presented with a list of faculties (of which you could select one) then being presented with the sub-facet of departments that match the selected faculty.
You'd see something like the following after your initial search.
Faculty of Art
Faculty of computing
If you the selected Faculty of Art you'd then see the sub items for that faculty, and the other faculties would not display.
Faculty of Art [X]
I note from your initial post you've been attempting to set up multi select facets. Firstly when setting up multi-select I would recommend you use the faceted_navigation_v2 library that's available from the Funnelback community site - this provides a bunch of enhancements to the way faceted navigation works, and allows you to use the same code for both single and multi-select facets.
There are limitations when using multi-select facets though, the main ones being that they don't support any hierarchy and the second one being you lose any facet counts.
The other approach you could use is to define a facet for each faculty - this would require a metadata field for each faculty that had the department values as the categories.
In this way you would have a flat faceted navigation structure, with a facet defined for each faculty.