Question

Which part of speech is the underlined word?

That's what a fast is—a period of time during which you do not eat.(fast being the underlined word)

A.
noun

B.
adverb

C.
conjunction

D.
preposition

Answer 1

Are you asking whether "fast" is a noun, adverb, conjunction, or preposition? If yes, well "fast" is an adverb. Hope it helped!

Answer 2

The word fast can be used as a number of parts of speech - it can be an adjective, an adverb, a verb, and a noun.
In this sentence, however, the word fast is used as a A. noun.
The safe way to check whether I am correct is to see if there is any article before that word - and since there is (the article "a"), you can trust me I am correct. :)