Is this red oak or white oak hardwood flooring?
It's impossible to say for sure from your picture since it is already stained.  But generally speaking the approach to this is trial and error with scrap pieces. You'll want to make sure the piece of totally dry before comparing the colour and it can look quite a bit different when wet.

It's unlikely you will get an exact match even using the exact same product since wear and tear and UV take their toll on floors.  The only way to get an exact match across both floors is to refinish the old and new with the same product.