The correct answer is A. Hang.
To lynch someone is to kill them by hanging, usually without a trial. Lynchings are often carried out by a mob, and they are often motivated by racism or other forms of bigotry. Lynchings are a serious human rights violation, and they should never be tolerated.
Option B, madden, means to make someone crazy or insane. This is not the correct answer because lynching is not a form of madness. It is a form of violence.
Option C, kill, is a more general term than lynch. It can refer to any act of killing, whether it is carried out by a mob or not. However, in the context of the question, the most likely meaning of kill is to lynch someone.
Option D, shoot, is another more general term than lynch. It can refer to any act of shooting, whether it is carried out by a mob or not. However, in the context of the question, the most likely meaning of shoot is to shoot someone to death.