Mapp v. Ohio (1961) ruled that state law agencies could not use any evidence in state courts that had been collected in violation of the Fourth Amendment’s protection against "unreasonable searches and seizures."

The Supreme Court case, Gibbons v. Ogden (1824), relates to the Congressional power to exclusively regulate interstate commerce. Specifically it states that this power, granted to Congress in the Constitution, included the power to regulate commerce along rivers.

The Supreme Court case Korematsu v. United States (1944) upheld the right of the United States government to forcibly intern Japanese citizens and American citizens of Japanese descent during World War Two. The majority ruling found that the need to protect the nation during a time of war from espionage and treason outweighed the individual rights of Japanese citizens and American citizens of Japanese descent.

In the Supreme Court case Gideon v. Wainwright, the Supreme Court ruled that the state governments were legally bound by the Fifth, Sixth, and Fourteenth Amendments to provide legal counsel to a defendant who could not afford one. In doing so, they overturned a previous Supreme Court ruling in Betts v. Brady, which had stated that these rights did not always apply at the state level.

In McCulloch v. Maryland, the U.S. Supreme Court held that federal laws have supremacy over state laws, and that therefore the State of Maryland had no authority to interfere with or oppose the operations of a bank established by Congress.

The 1973 companion cases of Roe v. Wade and Doe v. Bolton involved the principles of a woman's rights to privacy and to make decisions concerning her own health, as well as the state's legitimate interests in protecting women's health and the potentiality of human life. In those cases, the Supreme Court extended the right of privacy to a woman's decision to have an abortion. The right of spousal consent in the areas of birth and abortion was dealt with in the 1992 case, Planned Parenthood v. Casey, where the Supreme Court overturned a state law requiring spousal awareness prior to abortions.

In Citizens United v. FEC, the Supreme Court defended the political speech and political contribution rights of corporations, unions, and not-for-profit organizations.

Gideon v. Wainwright [somewhat] famously incorporated the 6th Amendment's guarantee of representation even to those who cannot afford it (so-called indigent ("poor") counsel).  There's also a movie about this case called "Gideon's Trumpets." 

The answer, "the right to be represented by the best . . ." may sound tempting, but it is not true. The state must provide you with counsel if you cannot afford it (if you want it, that is), but there's no requirement that your representation be the best.

The other answers are different Amendments that were not relevant to the case.

Brown v. Board is the correct answer. It was in this case that Chief Justice Warren declared unconstitutional segregation in public education. The language “with all deliberate speed” became nearly as famous as the case itself.

One precautionary note before continuing to the incorrect answers: technically speaking, there are TWO Brown v. Board cases—the first in 1954 (Brown I) the second in 1955 (Brown II). Brown I is the case that says segregation in public schools is unconstitutional. Brown II answers the question of “how fast should we remedy this problem” with “with all deliberate speed.” This is a hyper-technical distinction, but a relevant one nonetheless.

Although Plessy v. Ferguson may sound correct (hopefully it sounds familiar), it is not the correct answer. Brown v. Board actually overturns (that is, says it is incorrect) Plessy. More specifically, Plessy held that, so long as segregation was “separate but equal,” it was OK—that is constitutional. Brown directly contradicts that, saying “The ‘separate but equal’ doctrine adopted in Plessy v. Ferguson has no place in the field of public education.”

Gibbons is incorrect as it is a case dealing with Congress’ ability to regulate commerce.

Citizens United is incorrect as it is a case dealing with the interplay between the First Amendment and election contributions.

Ex parte Milligan is a case dealing with the suspension of habeas corpus during the Civil War.

Gibbons v. Ogden is the correct answer. To begin with, you should be able to eliminate one contender from the list: Brown v. Board of Education. Not only is Brown arguably the most famous case on that list, it is also the youngest (relatively speaking). Remember: the Supreme Court decided Brown in 1954! More importantly, Brown had nothing to do with the regulation of interstate commerce—Brown declared unconstitutional segregation in public schools.

Next, you should eliminate Plessy. The Supreme Court decided Plessy in 1896, long after Chief Justice Marshall’s tenure on the Supreme Court (and life, for that matter) was up. Moreover, Plessy—similar to Brown—dealt with race relations, rather than directly addressing interstate commerce. In fact, Plessy is the Supreme Court case which rather famously held “separate but equal” accommodations to be constitutional. Remember: Brown overruled Plessy!

Finally, we come down to the three cases all decided by the Marshall Court. (Remember: particular eras in the Supreme Court are referred to by the name of the presiding Chief Justice; thus, any case decided between 1830-1834 we would refer to as decided by the “Marshall Court” as Chief Justice Marshall presided during that time). Out of the three remaining, Barron v. Baltimore may be a tempting answer. But, remember that Gibbons had to do with a squabble started by the New York legislature. Because, somewhat obviously, Baltimore is not New York, the name of the case itself should give you a hint in the right direction. More importantly, however, Barron revolved around 5th Amendment issues—eminent domain, in particular (do you remember what ‘eminent domain’ means?).

That leaves only Gibbons and Marbury as the remaining answers. Marbury may be a tempting choice—it is arguably one of Marshall’s most famous (and probably confusing) cases, but it is not about interstate commerce! Marbury centers on the difference between “original” and “appellate” jurisdiction (do you remember the difference?).

Thus we are left with Gibbons, the one and only correct answer. The background of Gibbons is relatively interesting: in brief, it is about a state-chartered (a fancy term for “granted”) monopoly which ended up implicating the financial interests of Mr. Gibbons. More specifically, Gibbons had to pay an exorbitant sum to operate his steamboat ferry (which, importantly, ran from New Jersey to New York) in the waters of New York (because the legislature gave a monopoly to Ogden). Understandably, Gibbons was rather . . . steamed . . .  about this, hence this case. The short of it is that Gibbons won, because New York overstepped its authority by issuing such a monopoly; the Constitution gives the power to regulate “interstate commerce” (that is business—whether it be actual goods or people—in between states) to Congress. Because Gibbons ran a ferry in between New Jersey and New York, New York’s prohibitions implicated interstate commerce.