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You have to use the balanced chemical reaction in order to solve this problem, which is CO(g) + 3H2(g) <--> CH4(g) + H2O(g). I'm assuming that you remembered to divide the moles of CO and H2 by the volume of the container to get the initial concentrations of CO and H2. The initial concentrations of CH4 and H2O are 0 since they are not given. Since you know that there are 0.478 mol CH4 at equilibrium, using the balanced chemical equation, you can infer that there are 0.478 mol H2O at equilibrium because of the 1:1 ratio (remember to divide by volume!) and that the moles of CO decreased by 0.478 (1:1) and the moles of H2 decreased by 3*0.478 (3:1). After that it's all hard numbers so you can just plug them into the expression for Kc, assuming that you raised the concentrations to their appropriate powers.
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