Why can we ignore Lyle's share of the money?
Imagine that there's a nice stack of money on the table to be split between the friends. Lyle grabs his cash and leaves the room. Now we're left with Bob and Chloe in the room. We've got a (smaller) stack of money on the table. We know that Chloe ends up with the remaining $32, so all we really need to know is how much money was thereafter Lyle left.
To make this clearer, you might try working backward using the 32. Directly before the $32 were left on the table, Bob took 1/3 of the money that was there. That means there must have been $48 on the table before Bob took the 1/3, since 48 - (1/3)*48 = 32. And before that, he had taken $4. Add that onto the 48, and we know that there were $52 before Bob took his share. 52 - 32 = 20