Answer:
boxed{8.67}.
Explanation:
If Ali colored 2/10 of the rope red, then the length of the rope that is colored red is 2/10 x 10 = <<2/10*10=2>>2 meters.
The remaining length of the rope that is colored green is 10 - 2 = <<10-2=8>>8 meters.
2/3 of the rope is colored green, which means the colored green rope has a length of 2/3 x 10 = <<2/3*10=6.666666666666667>>6.67 meters.
Therefore, the length of the rope is 2 + 6.67 = <<2+6.67=8.67>>8.67 meters. Answer: \boxed{8.67}.