A team has finished a game with 6-14 singles and extra-base hits 2 times since 1897, most recently Atlanta Braves on 21 May 2021. That is about one every 221,502 team-games.
Box score for the most recent one ↗
6-8 6-9 6-10 6-11 6-12 6-13 6-14 7-5 7-6 7-7 7-8 7-9 7-10
The whole distribution — Singles and Extra-Base Hits · All 18 shapes