The correct answer is: D. had / were looking
The past perfect tense is used to talk about an action that was completed before another action in the past. In this case, the first action is “we had dinner with them” and the second action is “they were looking for a new house.” The past perfect tense is formed with the past participle of the verb (had looked) and the past tense of the auxiliary verb “to have” (had).
The past continuous tense is used to talk about an action that was happening at a specific time in the past. In this case, the specific time is “the last time we had dinner with them.” The past continuous tense is formed with the past participle of the verb (looking) and the present tense of the auxiliary verb “to be” (were).
The other options are incorrect because they do not use the correct tenses. Option A uses the present perfect tense, which is used to talk about an action that started in the past and continues into the present. Option B uses the past progressive tense, which is used to talk about an action that was happening at a specific time in the past. Option C uses the present progressive tense, which is used to talk about an action that is happening now. Option E uses the simple present tense, which is used to talk about an action that happens regularly or repeatedly.