Lots of possible approaches here.
One approach is to TEST the answer choices to see which one satisfies the given information. I'll leave that one to you.

Another approach is to use some algebra.

Since both pieces of information reference Josh.....
Let J = the amount of money Josh has.

Josh has 3/4 as much money as Doug
Another way to say this is, "Doug has 4/3 as much money as Josh"
So, (4/3)J = the amount of money Doug has.

Josh has three times as much money as Brad
Another way to say this is, "Brad has 1/3 as much money as Josh"
So, (1/3)J = the amount of money Brad has.

Josh, Doug, and Brad have a total of $72 between them
So, we get: J + (4/3)J + (1/3)J = 72
Multiply both sides by 3 to get: 3J + 4J + J = 216
Simplify: 8J = 216
Solve: J = 27

Since (4/3)J = the amount of money Doug has, we can plug in 27 for J to get:
Doug's money = (4/3)(27) = 36

Answer: E