I'm not quite sure how to explain this, so I'll do my best. We can reduce the initial information to figure out how many lawns 1 teenager can mow in 1 hour. Given that 3 teens mowed 3 lawns, it's 1 teen/lawn. They are working at a rate of 1 teen can mow 1 lawn in 3 hours.
Now the second part. If 1 teen can mow 1 lawn in 3 hours, 6 teens can mow 6 lawns in 3 hours. Given that there are 9 hours and that 9 hours / 3 hours = 3 , 6 teens can mow 6 (*3) lawns in 9 hours, or 18 lawns.
Hope that helps, there's a link below which has similar problems.