Final answer:
African American men received the legal right to vote after the Civil War, with the 15th Amendment, and African American women alongside men could legally vote nationwide after the Voting Rights Act of 1965, which removed major barriers to voting.
Step-by-step explanation:
African Americans gained the legal right to vote after the Civil War with the ratification of the 15th Amendment which granted black men the right to vote. However, it wasn't until the Voting Rights Act of 1965 that significant legal barriers at the state and local levels that prevented African Americans from exercising their right to vote were removed. This law prohibited discriminatory voting practices that had been responsible for the widespread disenfranchisement of African Americans in the United States.
Particularly, the Voting Rights Act of 1965 outlawed literacy tests and authorized federal oversight and enforcement in areas with a history of voting discrimination. African American women, alongside black men, were able to legally vote in every state thanks to this landmark legislation. The act was a significant victory for the civil rights movement and marked a major milestone in the struggle for racial equality in America.