Backgammon best strategy for clearing my home
The logic of finding the “general rule” in these situations is flawed and will lead to potential mistakes. There are positions where you have to move the highest or the lowest number and need to be able to quickly calculate the numner of dice combinations that are favourable or not for your next roll.

In your example, if you leave the checkers at 6,1 points: you need all sixes (11 combs) plus 55,44,33,22 (4 combs), total of 15.

If you however leave the checkers on 4,3 points, you need 65,64,63,54,53,43 (12 combs) plus 66,55,44,33,22 (5 combs) for a total of 17 rolls. The latter play is superior.

Just in case one wonders why not always move the highest point, consider the example of having two checkers on 5,3 with a need to play a deuce. if your move is 5-3, leaving checkers on 3,3 you will clearly lose more games than if you have moved 3-1, receiving the position of 5,1. I will let you calculate the combs and compare.