The question is:

Let Jesse be x years old.

Let that be y years ago.

So y years ago, Jessie was x-y, and James' 
age now, 24, is twice that,

So 24 = 2(x-y)  

Now we ask: What else was true y years ago? 

James was 24-y

And also, y years ago,...

So James' age then, which was 24-y equals 
Jesse's age now, which is x years.  

So 24-y = x

We have this system of two equations and 2 unknowns.



Solve that and get x=18, y=6.

So Jesse is 18.

Checking: 6 years ago Jesse was 12.  

James is now 24, which is twice as old as Jesse was
then, which was 12.

Also, 6 years ago, James was 18, and that's how 
old Jesse is now.   
  
So it checks.

Edwin