Does a Facebook video show President Joe Biden crying and leaving a press briefing, only to come back and ask former President Donald Trump to return? No, that's not true: the video is clickbait and shows footage of a Pentagon press briefing. The video does not feature Biden at all.
The claim appeared in the title of a Facebook video (archived here) published on August 22, 2021. The title of the video read:
Biden cries and leave briefing after RIDICULOUS lie...asks Trump return in SHOCK
This is what the post looked like on Facebook on August 24, 2021:
(Source: Facebook screenshot taken on Tue Aug 24 17:15:46 2021 UTC)
The video, which only shows an excerpt of a Pentagon press briefing from August 21, 2021, about the Taliban seizure of Afghanistan, does not include Biden. The transcript of the press briefing can be found here (archived here) and also does not include commentary from Biden.
The headline of the video appears to be an example of a tactic used by Facebook pages to increase their traffic and follower cohort by enticing people to click.