Organic Chemistry Lab, Banana Oil?

"The right hand side of the equation" just means the product side. You were right about removing the product. If you remove the product while the reaction is going than the equilibrium will shift to the right or products side. I did this lab when I was in organic chemistry and I'm pretty sure you had to evaporate the banana oil out while the reaction was preceding which will, by Le'Chatlier's principle shift the reaction towards the right.