What term refers to inquiring in a nosy manner or snooping?

The term that refers to inquiring in a nosy manner or snooping is "Pry." This word implies a sense of intrusiveness or uninvited interest in others' affairs, often associated with a lack of regard for privacy. When someone is prying, they are attempting to uncover information that isn't readily shared, highlighting a curiosity that can be perceived as intrusive.

The other terms do not convey this specific meaning. "Quell" refers to suppressing or calming something, often used in the context of emotions or unrest. "Quaff" means to drink deeply, typically used in relation to consuming beverages, especially in a hearty manner. "Quack" generally refers to a fraudulent practitioner of medicine or someone who pretends to have skills or knowledge they do not possess. Therefore, "Pry" is the only term among the choices that explicitly indicates a nosy or intrusive inquiry.