What part of speech is back in you came after a while?

The word "back" in the phrase "you came back after a while" is an adverb.

Here's why:

* It modifies the verb "came". Adverbs tell us how, when, where, or to what extent something happens.

* "Back" indicates the direction of the action. It tells us that the person returned to a previous location.

Let's break down the phrase further:

* You: Pronoun

* Came: Verb

* Back: Adverb

* After: Preposition

* A while: Noun phrase (functioning as an adverbial phrase)