A team has finished a game with 12-12 singles and extra-base hits 1 time since 1897, most recently Cincinnati Reds on 13 July 2019. That is about one every 443,004 team-games.
Box score for the most recent one ↗
12-6 12-7 12-8 12-9 12-10 12-11 12-12 12-13 13-0 13-1 13-2 13-3 13-4
The whole distribution — Singles and Extra-Base Hits · All 18 shapes