2-away 2-away is a weird match score. If both players play correctly, it is inevitable that the cube will be turned to 2. That is because we don’t need to be concerned with the value of cube ownership at this score - owning the cube has no value. Theoretically it is correct to double any position where you have a greater winning chance than your opponent (gammons obviously don’t matter)
In practice, correct cube handling at this score is to double if you have ANY market losing sequence. In this position I would think black rolling 11, hitting two white checkers and making the five point followed by a white 66, 55 or 65 would be a market loser for black, and the reason for the double.
In practice, if I’m playing someone I know won’t screw up the cube action ina 2-away 2-away spot, I usually just turn the cube at first opportunity. That way I won’t screw it up and I can just focus on the checker play at double match point. You don’t really lose anything by doing this - it’s going to be a double/take at some point anyway regardless of who does the doubling.