。
Didn't you hear the voices from the next room?
Literal
Next [of-の] room [of-の] voices [subject-が] did-not-hear [question-か].
隣の部屋 ('the next room, neighboring room') — 隣 with の attaches to 部屋. 聞こえる ('to be audible, can be heard') is the spontaneous-perception counterpart of 見える ('to be visible, can be seen'), taking が on what's heard. ませんでしたか is the past polite negative question.