Final answer:
The federal government utilized military intervention, among other methods, to establish law and order in the American West.
Step-by-step explanation:
The method that the federal government employed to bring law and order to the West in U.S. history was A) Military intervention. This includes establishing forts, engaging in military campaigns against Native American tribes, and protecting settlers. However, the government also used other methods over time such as diplomatic negotiations, economic incentives, and passing legislation like the Homestead Act to encourage western expansion. Acts like the Indian Intercourse Acts exemplify the legislative approach to control and regulate interactions with Native Americans.