Excel count text in column match date only

I was going to say:

=SUMPRODUCT((Open_Date>=A9)*(Final_Status="Closed"))

BUT

You will have to correct one of your named ranges so that they both have the same ending row. As is, one named range is longer than the other.

I should point out that ALL of the dates in your sample DO match your criteria so ALL of the "Closed" values ARE being counted. If you change one of those dates to a lesser value you will see a reduction in the formula's return.