In this question, we have to find the number of moles needed of CH4 to burn 3.7 moles O2, and we can do that by looking at their molar ratio:
CH4 + 3 O2 -> 2 CO2 + 2 H2O
The molar ratio between CH4 and O2 is 1:3, which means that we need 1 mol of CH4 for every 3 moles of O2, therefore if we have 3.7 moles of O2, we will need:
1 CH4 = 3 O2
x CH4 = 3.7 O2
3x = 3.7
x = 3.7/3
x = 1.23 moles of CH4 are required