Hello there! Get ready as we delve into an exciting challenge involving list manipulation, combinatorial logic, and programming expertise. This challenge is about finding combinations in a given list where the sum equals a specified target value. Are you prepared for this intriguing quest? Great! Let's embark on this journey into the realm of problem-solving and number theory.

Here's the task ahead: You have to write a Kotlin function that accepts a list of distinct integers and a target sum as input. The goal is to identify exactly four numbers in the list that, when summed, equal this target. If there are multiple sets that fit this condition, your function should return any one of them. If no such quartet exists, the function should return an empty list.

Consider this list as an example: listOf(5, 15, 2, 7, 8, 4). If your target sum is 24, one four-number set that adds up to this value could be listOf(5, 7, 4, 8).

The input list will contain at least 4 and at most 1,000 distinct integers. The input integers will range from $-10^6$ to . The target sum will also be within the same range. The solution must evaluate within a time limit of 3 seconds.