Based on the given chemical reaction, it can be said that the equation is balanced. To get the amount of Hydrogen needed, back calculation can be done. From 192 g of water, it can be related to its molar mass to convert to the amount of mol. Based on the equation, 1 mol of H2 is equivalent to 2 mol water, by this the amount of H2 needed can be calculated by multiplying to the molar mass (18 g/mol). Below is the calculation:
192 g H2O*(1 mol H2O/18 g H2O)(1 mol H2/2 mol H2O)*(2 g H2/1 mol H2) = 10.67 g H2