Which of the following statements best describes a change that impacted african americans in the 1950sin the 1950s, more and more homes had a television mostly due to which of the following?

I'll answer your first question, because I've seen the answer choices elsewhere.  For your second question, maybe give the answer options in a comment.  

What change impacted African Americans in the 1950s?

Correct  Court cases challenged the legality of discrimination.

I'll mention key court cases after debunking the other answers in the list.  Truman's desegregation of the armed forces happened already in 1948, and impacted only those in the armed forces, rather than all African Americans.  The suburbs were NOT welcoming toward African Americans, and they remained in living mostly in urban centers.

As to key court cases of the 1950s regarding discrimination:

1950: Sweatt v. Painter and McLaurin v. Oklahoma State Regents.  In these cases, the Supreme Court said segregation of African American students in law and graduate schools was unconstitutional.  This was the start of challenging "separate-but-equal" policies.

1954: Brown v. Board of Education.  Firm decision that "separate but equal" policies were unconstitutional across the education system.  Chief Justice Earl Warren, speaking for the unanimous opinion of the Court, said: “Separate educational facilities are inherently unequal.”  

1955: Brown v. Board II.  The Supreme Court directed that school systems must abolish segregation “with all deliberate speed.”

1956: The Supreme Court affirmed a lower court ruling that the segregation of the Montgomery, Alabama, bus system was illegal.  This was in reference to the bus boycott that had begun with the protest by Rosa Parks.

1958: Cooper v. Aaron.  The Supreme Court upheld the US Court of Appeals (8th Circuit) decision that resistance by local officials and threats of violence in the community did not  justify delaying desegregation.  This followed in the wake of the Little Rock Nine (a group of black students) seeking enrollment in LIttle Rock Central High School.

the answer is option a.

the correct answer is d