It's because you ultimately add up all three equations to get the overall equation. When you flipped line a, you put H2O on the left. Line b also has H2O on the left. Line c has no H2O in it, so in total (adding all three equations together) you have 2 H2O on the left - just as in the overall reaction equation.

After flipping line a, you'd have another H20 on the left sift of the equation, so you'd have two total. Thus, no need to multiply. :D