Kathy is 6 years younger the Bill. Twelve years ago, Bill was twice as old as kathy was then. How old are they now?

k = Kathy's age now

b = Bill's age now

(1) k=b-6

(2) b-12=2 x (k-12)

(2) b-12=2k-24

(2) 2k-b=12

From (1)

(1) - k+b=12

Add (1) and (2)

k=18

and

(1) k=b-6

18=b-6

b=24

Kathy is 18 and Bill is 24

check:

(2) b-12=2 x) k-12)

24-12=2 x (18-12)

12=12

OK