Which amendment prohibits "cruel and unusual punishments"?

The amendment that prohibits "cruel and unusual punishments" is the 8th amendment. This provision is a critical aspect of the Bill of Rights, as it is intended to protect individuals from excessive bail, excessive fines, and particularly from punishments that are deemed inhumane or excessively harsh in relation to the crime committed. The phrase "cruel and unusual" has been the basis for many important Supreme Court cases regarding the treatment of individuals in the criminal justice system, influencing standards of decency in punishing crimes.

In contrast, the 6th amendment focuses on the rights of criminal defendants, including the right to a speedy trial and the right to counsel. The 10th amendment concerns states' rights and powers not delegated to the federal government, while the 12th amendment outlines the process for electing the President and Vice President. These amendments do not address issues relating to the treatment of punishments, making the 8th amendment the correct choice in this context.