It is 41.1g of one of the reactants is converted to 368g of the product. You have to determine how many moles of the product were produced. Then use the stoichiometry of the reaction to determine how many moles of oxygen you need to make that much water.
As a side note, the calculation does not require the 41.1g of hydrogen, except that the moles of water produced should not be more than the number you get when you convert the mass of hydrogen to moles (41.1g/2.008g/mol=20.47moles H2). I'll break the problem down into steps. It may look tedious, but with practice, it'll be easy enough to perform.
Step 1: Write the balanced chemical reaction: 2H2 + O2 -> 2H2O.
Step 2: Convert the mass of water to moles using mass divided by molar mass.
Step 3: Compare the ratio of water to hydrogen (the other mass they give you). Here, it's 2 H2 per 2 H2O, or 1 H2 per 1 H2O (1H2/1H2O).
Step 4: Convert the mass of Hydrogen to moles of hydrogen. Here, its 41.1g/2.008g/mol=20.47moles H2.
Step 5: Multiply your answer from step 4 by the ratio is step 3.
Step 6: Compare your answer from Step 5 with your answer from Step 2. If the answer from Step 5 is greater than (more than, larger than, or any other synonym for larger than) your answer from Step 2, then one of your calculations are wrong. Otherwise, carry on to step 7.
Step 7: Get the ratio of the product to the reactant you're trying to figure out; here, it's water and oxygen. There is 1 O2 consumed for every 2 H2O molecules produced, so use 1O2/2H2O.
Step 8: Multiply the answer from Step 5 by the ratio in Step 7. This will be the moles of oxygen consumed.
Step 9: Multiply the answer from step 8 by the molecular mass of oxygen.