Answer: 27.56 moles of hydrogen
Step-by-step explanation:
According to the law of conservation of mass, mass can neither be created nor be destroyed. Thus the mass of products has to be equal to the mass of reactants. The number of atoms of each element has to be same on reactant and product side. Thus chemical equations are balanced.

According to stoichiometry:
1 mole of ethane is produced by = 2 moles of hydrogen
Thus 13.78 moles of ethane is produced by =
moles of hydrogen
27.56 moles of hydrogen are needed to produce 13.78 mol of ethane.