The Mercy Rule
The entire first half is played no matter the score and the referee keeps a record (time and jersey number of the scorers) of all the scores during that time.
At halftime the referee verifies the score and if there is a 6 goal differential, the game is over.
The referee write a note on the game card to explain why the second half was not played. Maybe the score was 10-4 or 7-1.
If at halftime the goal differential is NOT 6, the second half starts. As goals are being scored the referee must keep track of the goal differential and as soon as there is a 6 goal differential, the game is over.
After the halftime, the goal differential can happen at any time. If the score was 5-0 at halftime and let’s say in the second minute of the second half the team with 5 goals scores another goal—the game is over at that time and the referee makes a note on the game. The referee writes the time the 6th goal was scored on the game card.
Example of an explanation: In the second minute of the second half #4 of team A scored a goal which made a goal differential of 6. The game was terminated at that time (10:35 a.m.) per district rule.
Referees get paid for the whole game no matter what. Also they should NOT continue to referee that game because it is no longer legal or sanctioned and the referee(s) could find themselves in trouble if a red card is issued (would it be valid?) or someone gets hurt (would there be any insurance?).