What is the meaning of "He should shake out his bed with the inside of his lower garment," and what is "the inside of the lower garment," and how should the shaking be done? Why was this specific phrase mentioned, and is this hadith authentic?

The aforementioned hadith is authentic, narrated by Al-Bukhari and others. Its wording, from Abu Hurayrah, is that the Prophet (peace be upon him) said: "When one of you goes to his bed, let him brush off his bed with the inside of his lower garment, for he does not know what might have come onto it after him..." Commentators on the hadith stated that the "inside of his lower garment" refers to its edge and inner border. The command to do so is for several reasons, including: maintaining the cleanliness of the outer garment, ease and modesty, reducing the exposure of one's awrah (private parts), and avoiding blowing with the hand to preserve its cleanliness or prevent it from encountering something disliked. Al-Hafiz mentioned in Al-Fath, quoting Al-Qurtubi, that the wisdom behind this brushing might be a special medical property that prevents animals from approaching, and this is supported by the command to brush three times. Its manner—and Allah knows best—is by lightly striking the bed with the garment.