You sign in to your personal computer with your Microsoft account and then you want to set up your computer as a trusted device to make changes to the account settings. Microsoft sends a code to your cell phone in a text message. You enter the code on a Windows screen. This type of authentication is called:

Mutual authentication

Explanation:

Based on the scenario being described within the question it can be said that this type of authentication is called mutual authentication. Like mentioned in the question this is a process in which two different entities link to each other in order to authenticate one another. Thus providing the user with extra security measures.