Answer:- d) Durable power of attorney
Explanation:-
Durable power of attorney is defined as document which allows principle for designating other person to act on behalf of principal legally. This permission is given in the situation where principal is no longer in state of making decision due to inability, disability, illness etc or other reasons.
According to the question,son's designation for making decision for her mother is allowed through durable power of attorney so that he can act on behalf of old home client.
Other option are incorrect because power of attorney, living will and designated signature person is not the legal factor for opening son's designation on making decision. Thus, the correct option is option(d).