A team has finished a game with 6-13 singles and extra-base hits 6 times since 1897, most recently Minnesota Twins on 20 April 2019. That is about one every 73,834 team-games.
Box score for the most recent one ↗
6-7 6-8 6-9 6-10 6-11 6-12 6-13 6-14 7-5 7-6 7-7 7-8 7-9
The whole distribution — Singles and Extra-Base Hits · All 18 shapes