What outcome of the war does the cartoonist predict?

The correct answer is: "schools must desegregate schools must integrate"

Brown v. Board of Education was a landmark decision issued by the US Supreme Court in 1954, which  declared segregation to be unconstitutional and overturned the decision formerly reached in Plessy v. Ferguson. It was considered a major victory connected to the Civil Rights Movement.

Plessy v. Ferguson was a landarmark decision enacted by the US Supreme Court in 1896 which allowed segregation in public schools, declaring that it did not violate the Equal Protection Clause, guaranteed by the Reconstruction amendments to the US Constitution (14th and 15th), as long as the facilities provided for black and white students were equal in terms of quality. Segregation was not unconstitutional, as long as the "separate but equal" criteria was fulfilled.