下毒手 is a verb-object compound (离合词) meaning to deliberately commit a vicious or fatal act against someone, often after plotting. The verb 下 ('to apply') and the object 毒手 ('murderous hand') can be separated — for example, you can say 下了毒手 ('carried out the vicious attack') or 下过毒手 ('have committed such an act'). It carries a strong sense of premeditation and cruelty, and is typically used in narratives about villains, schemes, or ruthless actions.