Final answer:
The Third Amendment, which protects against the quartering of soldiers in private homes, has not been applied to the states through the due process clause of the Fourteenth Amendment, making it the answer to which amendment is not incorporated against the states.
Step-by-step explanation:
The question relates to which of the amendments enumerated in the Bill of Rights is not applied to the states through the due process clause of the Fourteenth Amendment. Looking at the options provided and understanding the history of their application, the Third Amendment is the correct answer. This amendment, which protects citizens from having soldiers quartered in their homes without their consent, has not been incorporated against the states via the Fourteenth Amendment. Options (a), (b), and (d), namely the Second, Fifth, and First Amendments, have been incorporated to apply to the states. Option (e), the Fourteenth Amendment itself, is not applicable since it is the mechanism by which other rights are incorporated against the states, not a right that needs to be applied through itself.