How many moles of water will produced at equilibrium be if there is 1.0 mole of carbon dioxide formed at equilibrium?

2 C2 H6(g) + 7 O2(g) <==> 4 CO2(g) + 6 H2 O(g)
...
[CO2]^4[H20]^6/[C2 H6]^2[O2]^7

You are making it way too complicated.

1 mole CO2 x (6 moles H2O/4 moles CO) = ??moles H2O