Hint:
Assume the total candies in the filled jar to be 'x'
Mr Peterson took third i.e., 1/3 x
Remaining candies after Mr. Peterson took candies = x - 1/3 x = 2/3 x
Mr Luch took 20 candies
So, remaining candies after Mr Luch took candies = 2/3x - 20
Mr Ming ate the remaining half i.e., (2/3 x - 20)/2
So, remaining candies after Mr Ming took candies = (2/3 x - 20)/2
Mr Rea took 8 candies.
So, remaining candies = (2/3 x - 20)/2 - 8
Finally, the remaining candies = 1
So,
(2/3 x - 20)/2 - 8 = 1
Now, Solve for X