The correct answer to this question is A. It was the Brown v. Board of Education decision that was handed down in 1954 which banned racial segregation in schools in the United States.
This case was brought as a way to try to overturn the Plessy v. Ferguson decision that had been handed down in 1896. That decision held that racially segregated facilities of all sorts were legal so long as they were equal to one another. This was the "separate but equal" doctrine.
In Brown, the Court held that separate educational facilities could never be equal. This was because racial segregation, by its nature, stigmatized black students. Therefore, the Court held segregation could no longer be legal.
The correct answer is A: Brown vs. Board of Education. Previously, in 1896, the Court had issued the infamous Plessy vs. Ferguson decision, which said that separate facilities did not violate the Equal Protection Clause of the 14th amendment so long as those facilities were "equal." Hence the famous "separate but equal" doctrine. Schools, and other public facilities thus had the blessing of the court to remain segregated.
Brown vs. Board of Education, a combination of cases which actually began in Williamsburg County, South Carolina, but combined into the Topeka Kansas case held that separate schools were inherently unequal and had no place in American society. The decision by the Court was unanimous. Even so, it took over 35 years for equal education to even approach reality.