A team has finished a game with 6-16-3 runs-hits-errors line 34 times since 1897, most recently Boston Red Sox on 6 May 2012. That is about one every 13,029 team-games.
Box score for the most recent one ↗
6-15-2 6-15-6 6-15-4 6-15-0 6-15-5 6-15-7 6-16-3 6-16-1 6-16-2 6-16-5 6-16-0 6-16-4 6-16-6
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes