Question 971661
girl's age now is x
Her mother's age now is 3x

x-6 was her prior age 
(x-6)*9 was her mother's age.

The difference in their ages is 2x and always has been.

Therefore, (x-6)*9 - (x-6) =2x
9x-54 -x +6 =2x
6x=48 by collecting terms and moving the constants to the other side.

x=8
mother is 24

6 years ago, girl was 2
mother was 18