Hello Lindsay, I'd be happy to help you answer this question!
2KClO3 --> 2KCl + 3O2
Both sides of the reaction are balanced, because there is the same number of both elements on the product and reactant side of the reaction. Therefore the coefficients will provide the ratio. For every 3 moles of O2 that are produced there are 2 moles of KClO3 that decompose . Therefore the ratio is 3 to 2. Starting with 18.0 moles of KClO3 you will get:
mol KClO 3 x 3 mol O2 = 27.0 mol O2
mol KClO 3
Your answer is 27.0 mol O2