The Voting Rights Act of 1965 helped to ensure that African-Americans had the right to vote as promised in the 15th amendment of the Constitution. To do this, the federal government oversaw elections in the South and outlawed literacy tests and poll taxes for African-American voters.
The one thing that this did not affect was greater support for Kennedy's domestic plans (Letter D). This is because Kennedy was not in office in 1965. John F. Kennedy was assassinated in November of 1963. His Vice President, Lyndon B. Johnson was president during 1965. This is why letter D is correct.