You have to show us your units. Based on the way you've set up your problem, my guess is that somehow in your lab, you obtained the measurement that one mole of electrons had a total charge of 1.1*10^8 coulombs. So your starting measurement is 1.1*10^8 coulombs/mole. Is that right?
Now you are trying to determine the total number of electrons in a mole, using the charge on an electron which is 1.60*10^-19 coulombs/electron.
So as Curiouscat asked, why are you including Avogadro's number, and what units are you attaching to it? The only units that would make sense in context would be electrons/mole, and that is the value you are trying to calculate! All you should need to do is to divide your value for coulombs/mole by your value for coulombs/electron - the coulombs cancel, and you are left with electrons/mole.
So go back to your experiment and attach the units - what value were you actually measuring? 1.1*10^8 what?