Which of the following is a method for terminating an agency by actions of the parties?

Mutual agreement is a method for terminating an agency by actions of the parties because it involves the agreement of both the principal and the agent to end their contractual relationship. This type of termination reflects the voluntary aspect of agency relationships, where both parties can decide to conclude their arrangement for various reasons, such as a change in business strategy, dissatisfaction, or the completion of the purpose for which the agency was created.

The other options represent different concepts. Approval by a third party does not directly influence the agency relationship between the principal and the agent, as the termination must be initiated by the parties involved rather than an outside influence. Providing additional authority usually serves to extend the agent's responsibilities rather than terminate the agency. Changing the agent's position can also indicate a modification in the agency's terms or scope rather than a termination of the relationship. Thus, mutual agreement is clearly the method that highlights the joint decision of both parties to end their agency relationship.