The Right to the Streets of Memphis was written by Richard Wright, born 1908, who was an African-American writer and it tells about his childhood. Strangely it isn't written anywhere (on the internet) that Wright ever lived in Memphis, so maybe it's a metaphor for some other experience he had as a child. Wright wrote much, particularly novels, short stories, poems and non-fiction, and often they would content racial themes.
The story can be disputed into two parts. In the first part, we hear about a family that hungers, while the father is away, and in the second part, we hear about how their mother gets a job and "leaves" their father, and gives one of the sons(the writher) the mission to be the head of the family. We hear about how he gets money from his mother to buy groceries, but each time he goes, he gets attacked by a gang of boys and he's money gets stolen. His mother tells him to beat them if they bother him again, and gives him a stick. He successes to beats them and wins "The rights to the streets of Memphis".
Their father is the only one who can provide food to the family, but he's never home. He probably been taking as a slave or been killed, because of the high slave trades in the first of the 1900's.
When the mother gets a job as a cook, and is able to feed the family again. When her kids ask where their father is, she's replying that they "...were too young to know".