Final answer:
The landmark legislation signed by President Lyndon Johnson on August 6, 1965, that guaranteed black Americans the right to vote is known as the Voting Rights Act of 1965.
Step-by-step explanation:
On August 6, 1965, President Lyndon Johnson signed a landmark legislation guaranteeing black Americans the right to vote. The name of this significant legislation is B) Voting Rights Act. The Voting Rights Act of 1965 prohibited states and local governments from passing laws that discriminated against voters on the basis of race, thereby outlawing literacy tests and other barriers to voting that had previously prevented ethnic minorities from voting. By 1967, the majority of African Americans had registered to vote, thanks to this act.