how many moles of CO2 can be produced from 15 moles of Fe2O3?

Write the equation and balance it.

Use the coefficients in the balanced equation to tell you what the ratio is and use logic to determine mols CO2 produced. Post your work if you get stuck.

I balanced to 2Fe + 3CO2. but do not know where to go from here

I would use the dimensional analysis approach.

Start with what you have (in this case 15 mols Fe2O3) and convert to mols CO2.
15 mols Fe2O3 x (3 mols CO2/2 mols Fe2O3) = ??
Notice that the 3 mols CO2 and 2 mols Fe2O3 come form your equation. Also notice that mole Fe2O3 you start with cancel with mols Fe2O3 in the denominator of the fraction leaving the unit mol CO2 left (and that is what you want from the problem).
For your next problem, convert mols CO2 to grams CO2. mols = g/molar mass.

23 mols of CO2

If I rounded 22.5 mols [15*(3/2) = 22.5], I would round to 22 (because I always round to the even number if the last number is a 5). But your answer is not wrong. Some people always round up. Follow the practice of your teacher.

To determine how many moles of CO2 can be produced from 15 moles of Fe2O3, we need to examine the balanced chemical equation for the reaction between Fe2O3 and CO2.

The balanced equation for the reaction is:

Fe2O3 + 3CO2 → 2Fe + 3CO2

From the balanced equation, we can see that for every 1 mole of Fe2O3, 3 moles of CO2 are produced. Therefore, we can set up a ratio to calculate the number of moles of CO2 produced from 15 moles of Fe2O3:

15 moles Fe2O3 * (3 moles CO2 / 1 mole Fe2O3) = 45 moles CO2

Therefore, 15 moles of Fe2O3 can produce 45 moles of CO2.