Mrs May strikes the cue ball twice, a clear foul.
The Italian prime minister challenged Ms May to a game after the first day of a summit between the European Union and Arab League countries.
A previous video posted on Twitter shows him explaining the rules to her.
“I’ll have a lot of support but I’ll be hopeless,” she says as he hands her a cue.
“You’ll have to show me how.”
Gavin Barwell, Theresa May’s chief of staff, then gets involved by showing her how to position her hand and how to hold the cue.
Earlier on Sunday, Ms May delayed a meaningful vote on the final Brexit deal, but insisted one would be held by 12 March.