The audio starts with some Ḥadith corrections and explanations from a previous class. The lecture starts at approximately: 9:20.
Abū Ḥurayrah (raḍī Allāhu ʿanhu) mentioned that he noticed that when the Prophet (ṣallallāhu ʿalayhi wa-sallam) prayed he would leave a gap (silence) between the takbīr (saying, “Allāhu Akbar”) and the recitation of al-Faṭiḥah. So he asked him, “What is it that you say during that time?” The Prophet (ṣallallāhu ʿalayhi wa-sallam) said “I say: ‘O Allāh separate me from my sins with the distance that you have separated the east from the west. O Allāh, purify me from my sins as a white thawb is purified from dirt. O Allāh, cleanse me of my sins with water, snow, and hail.'” (Collected by al-Bukharī and Muslim.)
There are other duʿāʾ that can be used at the beginning of the prayer as well. Ustadh Mūsá Richardson mentions them and the Āḥadīth from which they were derived. Some of them are specific to be said at night.
One thing we should note or observe from this Ḥadīth is that Abū Ḥurayrah was very astute. He would notice things that other people did not. He was the narrator of most Ḥadīth. We should be wary of people who revile him and tell lies about him to distance the Muslims from believing in what he reported and eventually turning the Muslims away from taking any Ḥadīth at all, instead of relying only on the Qurʾān.