Question

Yo termino la conversación y __________el auricular.

Answer 1

The answer would be colgar or cuelgo because your hanging up after your conversation.Hope that helps:)

Answer 2

We are going to translate the sentence into English:
 "I finish the conversation and hang up the earphone"
 The verb "hang up" in Spanish is "colgar"
 In the context of the sentence we use a conjugation of the verb "colgar" in Spanish.
 The conjugation is "cuelgo"
 Therefore, the complete sentence in Spanish is:
 Yo termino la conversación y cuelgo el auricular.
 Answer:
 Yo termino la conversación y cuelgo el auricular.