A team has finished a game with 6-4-3 runs-hits-errors line 3 times since 1897, most recently Detroit Tigers on 26 August 1969. That is about one every 147,668 team-games.
Box score for the most recent one ↗
6-3-0 6-3-3 6-4-7 6-4-1 6-4-2 6-4-4 6-4-3 6-4-0 6-4-5 6-5-2 6-5-1 6-5-3 6-5-5
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes