Let's set up some equations, using the initials as variables.
A = 6/7 K. Alex's age is 6/7 Kate's age
A-8 = 2/7K. Eight years ago, Alex's age was 2/7 as much as Kate's present age.
Let's use substitution, since A = 6/7 K we can substitute 6/7 K for A in the 2nd equation
6/7 K - 8 = 2/7 K
subtract 6/7 K from both sides
-8 = -4/7 K
multiply both sides by 7
-56 = -4K
Divide both sides by -4
14 = K
Kate is now 14 years old.