I was looking at a spinning reel that is raited for 8 lb. 10 lb. And 12 lb. Line on the spool. I want to put 6 lb. Fluorocarbon  line on it. Will there be a problem with using 6 lb. Test line?

It depends a couple of things but the short answer is you're probably fine.

 

What size reel you are using makes a difference - most 2000 and 2500 (and a few 3000) size reels would be perfect for 6lb.

 

What power is the rod? - a Medium fast might be ideal for 6lb but a Heavy probably not. 

 

What lures do you plan to fish? - baits around 3/8oz (maybe a fuzz heavier depending on the lure) would be ok but I wouldn't fish a 1/2oz jig on 6lb but 1/8oz with trailer would be great. 

The more line you wind on a spinning reel spool, the more the error in line management adds up. 

The error in line lay includes cone and hour-glassing, which can create wind knots. 

E.g., here's a spool that lays the rated 10-lb mono perfectly, but lays hour glass when you top the spool with thinner 16-lb braid (it has thicker backing beneath). 

While the result on the right isn't too bad to fish, the hour glass would be more severe and would be too bad to fish if you filled it with only the thinner line. 

More total line length = more total error. 

 

The best way to fish a lighter working line than the reel rating is to fill it most of the way with the larger line it's rated for as backing, then top it with the thinner working line.