Final answer:
Furman v. Georgia challenged the constitutionality of the 8th amendment protection from cruel or unusual punishment.
Step-by-step explanation:
The case that challenged the constitutionality of the 8th amendment protection from cruel or unusual punishment is Furman v. Georgia. In this case, the Supreme Court ruled that the arbitrary and inconsistent imposition of the death penalty violates the Eighth and Fourteenth Amendments and constitutes cruel and unusual punishment. This decision led to a nationwide moratorium on executions until the Supreme Court's decision in Gregg v. Georgia in 1976.