Which amendment extends the freedom of speech to the states?

The Fourteenth Amendment is the correct choice because it includes the Due Process Clause, which has been interpreted by the Supreme Court to apply the protections of the Bill of Rights, including freedom of speech, to the states. Initially, the First Amendment's guarantees applied only to the federal government. However, following the passage of the Fourteenth Amendment in 1868, the Supreme Court began to hold that states could not infringe upon certain fundamental rights. This process is known as "incorporation," and it has allowed the freedoms outlined in the First Amendment, such as freedom of speech, to be protected from state interference.

The other amendments listed do not relate to freedom of speech in the context of applying it to the states. The First Amendment guarantees freedom of speech at the federal level, but without the Fourteenth Amendment's incorporation doctrine, it wouldn't extend to the states. The Sixteenth Amendment establishes the federal income tax, while the Nineteenth Amendment concerns women's suffrage, neither of which addresses speech or the rights provided in the First Amendment.