Summing Totals Based on Criteria

In the example I want to have "F2" and "F3" to do a sum from column "C", but I need "F2" and "F3" to look at the data in column "A" before summing data in column "C".

I tried using countif, but it would error out or wouldn't pull the data the way I want it to. I need to take the logic and apply it to a much larger file.

Thanks in advance!