A team has finished a game with 14-8 singles and extra-base hits 48 times since 1897, most recently Chicago White Sox on 15 June 2022. That is about one every 9,229 team-games.
Box score for the most recent one ↗
14-2 14-3 14-4 14-5 14-6 14-7 14-8 14-9 14-10 14-11 14-12 14-13 14-14
The whole distribution — Singles and Extra-Base Hits · All 18 shapes