The correct answer is: out.
The phrase “turning out” can mean to leave a place, especially at night. It can also mean to become visible or known. In this case, the speaker is saying that their friend has a strange habit of leaving their house at odd hours.
The other options are not as likely to be the correct answer. Option A, “over,” could mean to turn something upside down. However, this does not make sense in the context of the sentence. Option B, “up,” could mean to turn something on or to increase the volume of something. However, this also does not make sense in the context of the sentence. Option C, “down,” could mean to turn something off or to decrease the volume of something. However, this also does not make sense in the context of the sentence.
Therefore, the correct answer is: out.