Hello and welcome to the forum.

For instance, I want the results to only show those that also meet the criteria of Status = "Active", Family = "Williams" and Product = "Slab".
I am assuming that you mean only count those not only show those. Try this:

=COUNTIFS(A:A,"Active",B:B,"Williams",D:D,"Slab")

Edit: Just realized that you are looking to count the number of unique names based on that criteria. 1 minute...