In ancient times, those who plotted rebellion were often given the supreme punishment.
Tips
usage
Formal/legal register. The verb 处以 (chǔyǐ, 'to mete out') very often partners with 极刑. In everyday speech you'd say 死刑 (sǐxíng, death sentence) instead.
memory
极 = 'extreme/ultimate', 刑 = 'punishment' - literally the most extreme punishment available.
