Hello! Get ready to dive into an intriguing problem involving list manipulation and combinatorial logic. We will explore the challenge of finding combinations in a given list that add up to a specific target value. Are you prepared for an exciting journey? Let's delve into the world of number theory and C#.

Here's your challenge: Write a C# method that takes an array of distinct integers and a target sum as inputs. The goal is to find exactly four numbers in the array that, when added together, equal the target. If multiple sets satisfy this condition, your method should return any one of them. If no such combination exists, the method should return an empty array.

Take this array as an example: [5, 15, 2, 7, 8, 4]. If your target sum is 24, a possible four-number set that adds up to this value could be [5, 7, 4, 8].

The input array will contain at least 4 and at most 1,000 distinct integers. The input integers will be in the range of -1,000,000 to 1,000,000. The target sum will also be within the same range. The solution must run within a time limit of 3 seconds.

The simplest solution is the brute-force approach that iterates over every quadruple combination of numbers in the array. The complexity of this approach is O(N^4).

Assuming performing an elementary operation in C# takes about 100 nanoseconds, then for an array with a thousand distinct integers, the time taken for an O(N^4) operation would be around 100 * 1000^4 = 10^{14} nanoseconds, equating to over 27 hours. This is clearly not efficient.