600 g
We've been told that 3.0 parts of carbon will react with 8.0 parts of oxygen. So let's use grams to say that 3.0 grams of carbon will react with 8.0 grams of oxygen to produce 11.0 grams of carbon dioxide (we get 11.0 grams of CO2 because of the law of conversation of mass. So 3.0 + 8.0 = 11.0).
Now we want 2200 grams of CO2. So divide 2200 by 11 to get 200. The value 200 represents 1 part. Now multiply that by 3 (because we want to use 3 parts of carbon) and you'll get 200 * 3 = 600 grams of carbon to get 2200 grams of carbon dioxide.