How did Frederick William I gain the loyalty of the Prussian nobles? Can you think of two other methods that absolutist rulers have used to
control their nobility? Which were most successful?

The correct answer to this open question is the following.

Although no options were provided, we can say the following.

Frederick William I gained the loyalty of the Prussian nobles because he gave them positions in the Prussian government and the military.

That was his way of getting loyalty and service to him. Frederick William I, King of Prussia from 1713 to 1740, knew that the nobles or Junkers (as they were known in that time) had ambitions and were full of greed, control, and power. So the best way to align them to his crown was to offer them positions of power and influence.

These have been the classic methods used by absolutists governments to "buy" the loyalty form wealthy families or even, the opposite factions of a government. The history of the European kingdoms was full of these situations.

c) troops march forward in close formation against newer, more accurate weapons

health and medicine because people are dying from not being healthy or not strong enough medicine