How much chemical you would need for a 9X12 area of carpet depends on several factors. One factor to look at is how heavily soiled is the carpet you're trying to clean. Naturally a lightly soiled carpet would require less solution than a heavily soiled carpet. Another factor to address is the manufacturers dilution ratio on the label of the product you've chosen to work with. Another factor is the cleaning method you'll be using. If you're using the hot water extraction (AKA steam cleaning) method, you'll need more solution than if you were performing a lower moisture method such as encapsulation.
I'll assume that if you've already chosen a specific product, you've also done your due dilligence to ensure that anyone who will be remotely close to the cleaning area is not allergic to your product of choice. I hope i've been of help to you.
Good Luck,
Dominick V. Cassano, President