How far back are you supposed to remember from your childhood?

It varies a lot. Some say they can recall events at 1 or 2 years of age. Children in elementary school challenge even their parents recall of the child's early events. By the time we are in our mid to late 20s not much prior to age 4 or 5 is recalled. Studies have compared actual known childhood events to our recall of those events. Recalled memories were found to be composites of several events, not one event.
Childhood. As a rough estimate, about 5 yrs onwards however this could vary individually.