Best answer is A. Equal protection under the law.
Answer B is also correct, in that the amendment is about the full exercise of the right of citizenship by all Americans. But the more specific answer, based on the final statement in the 14th Amendment, would be A) equal protection under the law."
Context:
The 14th Amendment guaranteed rights to life, liberty and property to all citizens born in the United States -- including those who formerly were slaves in states in the South. The amendment was ratified in 1868, following the Civil War, and was one of three amendments (XIII, XIV, XV) which were aimed at making black Americans full citizens of the USA.
After the Civil War ended, many Southern states still tried to block full access to citizenship rights by blacks. For instance, free public education was established in Southern states, but legislative actions barred black children from attending those schools. Blacks were also barred from voting, serving on juries, certain types of employment opportunities, etc. These were the sorts of things referred to as "Black Codes."
The 14th Amendment stated: <em>All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the </em><em>equal protection of the laws</em><em>.</em>