The fraternity and sorority students were required to wear their letters (meaning clothing or objects which showcased the Greek letters of their organizations) to the event. Which type of figurative language is "letters"?

The type of figurative language that is "letters" is synecdoche.

Explanation:

Synecdoche is a figure of speech which uses a part to represent the whole and vice versa. In the passage we are analyzing, the word "letters" was a part chosen to represent a whole. Instead of saying that the students were required to wear "the clothing or objects which showcased the Greek letters of their organizations", the author chose to use "letters" as a representative of all that. An example of synecdoche frequently found on the news is when it is said that the White House has issued a report. The White House is being used to represent the people who work in it, or even the President.