If you burn 57.9 g of hydrogen and produce 517 g of water, how much oxygen reacted?

In order to make water (H2O) out of hydrogen (H2), you also need OXYGEN (O2) gas.  So, first write a correctly balanced equation for this reaction.

2H2(g) + O2(g) ==> 2H2O

Now, convert 59.5 g of H2 to moles, then figure out moles of H2O and then moles of O2 used to do this.  

moles H2 = 59.5 g H2 x 1 mole/2 g = 29.8 moles H2

moles H2O formed = 531 g H2O x 1 mole/18 g = 29.5 moles H2O

So, the mole ratio of H2 to H2O is 1:1 meaning that the moles of O2 used will be 1/2 that amount.  This is the case because from the balanced equation you see that 1 O2 reacts with 2 H2 and produces 2 H2O. 

Amount of O2 used = 29.8/2 = 14.9 moles

the answer your looking for is c).