The reaction 2C + 2H2O --> CH4 + CO2 produces half a mole of methane from each mole of carbon that reacts if all the carbon takes part in the reaction.
But it is given that the reaction yield is 83%. This gives the number of moles of methane produced for each mole of carbon in the reaction as 0.5*0.83 = 0.415
The molar mass of carbon is 12 g/mol. 1616 g of carbon constitute 1616/12 = 404/3 moles of carbon.
The number of moles of methane produced from 404/3 moles of carbon reacting when the percent yield of the reaction is 83%, is equal to (404/3)*0.415 = 8383/150 moles.
As the molar mass of methane is 16, the grams of methane produced is 894.18 g.
894.18 g of methane is produced in the given reaction.