Answer: The words that correctly complete the sentence are "been living": "They have been living in Colorado for the last two years".
Step-by-step explanation: The Present Perfect Progressive Tense can only be formed with the modal verb "have" + "been" + the present participle of a verb, that is a verb ending in "-ing". In that way, the words that correctly complete the sentence are "been living" since "are", "be" and "were" cannot come after the modal "have" to form the Present Perfect Progressive Tense, which is mainly used to refer to a situation that started in the past and that is still in progress at present.