The argument made against brown v board of education by southern states was:
a. due process
c. the doctrine of nullification
b. equal protection
d. it was a states rights issue

Best  b. the doctrine of nullification

Explanation:

Two of the answers are essentially correct, because they are related.  Southern states were claiming a states rights issue when they invoked the doctrine of nullification.  After Brown v. the Board of Education was decided by the Supreme Court in 1954, a number of states in the South passed nullification measures in attempts to block implementation of the Court's decision and keep schools segregated in their states.

Cooper vs. Aaron (1958) was a specific case where state efforts to nullify a federal ruling was rejected.   William Cooper was president of the Little Rock, Arkansas, school board.  "Aaron and others" in the suit filed by the school board refers to the names of black children whose parents sued the school board over its refusal to allow integration of schools.  The Arkansas state argument was that the Supreme Court's decision was unconstitutional and interfered with states'  rights to set laws and policies in their states, and thus they had the right to nullify the implementation of Brown in their states.  

In Cooper v. Aaron, the Supreme Court denied the Arkansas School Board the right to delay desegregation of schools.  The Court asserted that the states cannot nullify Supreme Court decisions, ordering them to carry out the law of the nation even if they aren't in agreement with it.  

The doctrine of nullification has been attempted a number of times in US history, dating back to 1798, but the idea of states' ability to nullify federal law has never been upheld by federal courts.

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