The 12 he had left over at the end was the other one-third of
what he had before eating the two-thirds.  So 12 was 1/3 of 
those he had before starting eating.  So he had 3x12 or 36 before
starting to eat.

So those 36 he had before starting eating was the other 2/3 of what
he had before giving the one-third to Jack.  So since 1/3 is half
of 2/3, then he gave Jack half of 36 or 18.  So before giving those
18 to Jack, he must have had 36+18 or 54.

---

Now we check:

Jim gave one-third of his jellybeans to Jack, 

So Jim started with 54 and gave 54*1/3 or 18 of them to Jack.

That means he only had 54-18 or 36 left.

Then Jim ate two-thirds of the remainder, 

That means he ate 2/3 of 36 or 24.

So he had 36-24 or 12 left.
  
So 54 is the correct answer.

No algebra necessary!

Edwin