Question 163759
Let x be the bigger number and let y be the smaller number.
Then x - y = 12.
Also (2/5)x = 6 + (1/3)y.
Now, solve for either x or y in the first equation and substitute that value into the second equation. (You could also use elimination, but this is easier in this problem).
Let's solve for x.... 
Then x = 12 + y, and substitute this into the second equation:
(2/5)(12 + y) = 6 + y/3.  Now multiply out the left hand side:
24/5 + 2y/5 = 6 + y/3.  Now add the terms on the left hand side:
(24 + 2y)/5 = 6 + y/3.  Now get a common denominator for the right hand side:
(24 + 2y)/5 = (18 + y)/3.  You now have a ratio.  Cross multiply:
3(24 + 2y) = 5(18 + y).  Multiply out both sides:
72 + 6y = 90 + 5y.  Now solve for y in 3 steps.  
First, subtract 72 from both sides:
6y = 18 + 5y.  Now subtract 5y from both sides:
y = 18. Now, substitute this value for y into either equation in the first part to get your value for x.  I'll use the easy one:
x - y = 12
x - 18 = 12.  Add 18 to both sides to solve for x:
x = 30.
So... your answers are x = 30 and y = 18.

You can check your answers by plugging them into the second equation also.

Good luck!

JoeC