Which of the following words refers to a formal beginning of a term in office?

The word that refers to a formal beginning of a term in office is "inaugurate." This term is commonly used in political contexts, particularly during ceremonies when a new president, mayor, or other official takes office. The act of inaugurating not only marks the start of their term but also often involves a ceremonial aspect, highlighting the significance of the position and the responsibilities that come with it.

The other words have different meanings: "intervene" refers to becoming involved in a situation in order to alter the outcome, "instil" means to gradually impart an idea, feeling, or attitude, and "institute" refers to establishing something, such as a system or rule. Although "institute" and "inaugurate" might seem similar in context, only "inaugurate" specifically relates to the formal commencement of a term in office.