Conversion factors for a real life problem?

Yep, you're on the right track! Just compute for the value and that would be the gallons of oil saved per year.

(3.8 x 10^11 plastic bags / 1 year) x (4.3 x 10^5 gallons of oil / 1.8 x 10^8 plastic bags) = ________ gallons of oil per year

You want to know the amount of oil recovered per bag. If you know that 4.3E5 gallons are recovered per 1E8 bags, then 4.3E5 / 1E8 gives you how much oil is recovered per bag recycled. Then that number times 3.8E11 will tell you the total amount of oil saved if all the bags were recycled. So yes, what you said, 3.8E11 x 4.3E5 / 1E8 is equivalent to that, but it's kind of in a weird order. Doesn't matter though, multiplication is transitive so you can do it in any order.

But the oil saved if bags were banned altogether would be more than that since recycling doesn't recover every bit of oil.

whoa! I think you're using some wrong info here. It's gotta either be that you meant ban improper disposal of plastic bags, or you need the number of gallons of oil used to MAKE some number of plastic bags. recycling will not save as much oil as never producing in the first place.