I bought my daughter a 20" Huffy mtb at a garage sale last fall. It is a 6-speed (rear derailleur, no front). When I bought it, it was a three speed. I am very proud of my mechanical ability; I have got it to shift to 5 of the 6 cogs. The most effective form of adjusting the derailleur is to grab it and pull it very, very hard.
On the other hand, it cost $20 and will last this year. I will sell it for $15. It is heavy, but safe. She'll be ready for 24" wheels next year, if not 700c. I have never told her it's a POS, and she rides it a lot and likes it. It's sourapple green, which is important.