To figure out which reactant is limiting, divide the actual moles by the corresponding coefficient in the reaction:
CH4: 0.31 / 1 = 0.31 O2: 0.16 / 2 = 0.08
O2 is the lower number, so it is the limiting reactant. From the reaction we know it takes 2 moles of O2 to react with each mole of CH4. Therefore, for however many moles of O2 we actually have, half as many moles of CH4 will react. Since we have 0.16 mol of O2, only 0.08 mol of CH4 will react, leaving behind 0.31 - 0.08 = 0.23 mol of CH4.
Now convert back to mass (multiply by molar mass) to find the mass of CH4 remaining:
You have already gotten the balanced equation. And the ratio of mol number of reactants and production is the ratio of coefficient. So there is 6.4/8*11=8.8 mol oxygen needed. The mass is 8.8*32=281.6 g.