A team has finished a game with 0-6-8 runs-hits-errors line 2 times since 1897, most recently Cleveland Spiders on 9 September 1899. That is about one every 221,502 team-games.
Box score for the most recent one ↗
0-6-1 0-6-0 0-6-4 0-6-3 0-6-6 0-6-2 0-6-8 0-6-5 0-6-7 0-7-2 0-7-7 0-7-5 0-7-3
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes