I believe you may be referring to the landmark Supreme Court case Plessy v. Ferguson, in which the challenge was made to a Louisiana law that required separate railway cars for black people and white people. The plaintiff, Homer Plessy, argued that this segregation violated the Fourteenth Amendment to the U.S. Constitution, which guarantees equal protection under the law. However, the Supreme Court ultimately ruled against Plessy, establishing the doctrine of "separate but equal" and effectively upholding segregation. While the specific goals of those who challenged the railway-car law varied, many hoped to end the discriminatory practice of segregation and ensure equal rights for all Americans.