I have three moles of methane (CH4) on the reactant side of the reaction. Do I have enough information to determine how many moles of products I will have following a reaction? If not, what else do I need to know?

No, you do not have enough information to determine the number of moles of products following a reaction. In order to determine the stoichiometry of the reaction and calculate the number of moles of products, you need to know the balanced chemical equation for the reaction. The balanced chemical equation will provide the molar ratios between the reactants and products, allowing you to determine the number of moles of products that will be produced.