The best opening move for 6-4 in backgammon is 24/18 13/9. Splits and adds a builder. Watch it on the board, then read the idea behind it.
The idea behind the move
With 6-4 play 24/18 13/9. One back checker steps up to the 18-point to get free, and one checker from the 13-point comes down to the 9-point as a builder for the 5- and 4-points.
A close second choice: 24/14.
What comes next
Both checkers are lone and can be hit. The risk is accepted because it frees your back checkers and prepares points; a hit by your opponent also creates weaknesses for them.
How to read the move
A move like 24/18 means one checker goes from your 24-point to your 18-point. Points are counted from your side: 24 is the farthest, 1 is the deepest in your home board. “(2)” after a move means you play it with two checkers.