Confusion in solution for this Question regarding mole concept
16 g of dioxygen contains 16 g of oxygen atoms. To find out how much carbon dioxide is produced, you can either use a realistic description of the reaction, or you can go atom by atom. Either path gives the same solution, but the one chosen by the textbook is not modern chemistry, and makes some of us angry or sad.

My question is why not to use the reaction $\ce{C + O2 -&gt; CO2}$?

You should because that chemical equation describes the reactants and products much better than what the textbook has. It does not describe the mechanism (i.e. the steps to arrive at that net reaction), though.

What would the difference be in the answer.

Same numerical answer (unless you get confused because the reaction does not match the actual reactants).