Maximizing XOR HackerRank challenge
Couple of basic things with C#


Don't use Egyptian style Bracing, that's for Java.
Watch your indentation, I fixed it in the question.
Casing should follow basic C# standards

PascalCase for all Methods, Constants, and Property names
camelCase for everything else
Protected and public instance variables are UpperCamelCase (to avoid confusion with 3.2) as Jeroen commented 

You have more than enough newlines in the code, this can be distracting in your code.
From what I see of your Comments they are all unneeded

old code should be deleted
other comments are not needed to explain the flow of code or the purpose of the code because it is apparent what is going on with your code.



With these Variables I am not sure what was meant by the Underscore on them, they don't look private or look like properties, they should have a more meaningful name as well


   int _l;
   int _r;






   // We are only choosing 2 values out of any list of numbers
   int[] two_list = new int[2];



This seams like a waste of time to me, you want two numbers, not an array of numbers and not a list of numbers, so you should have two numbers.

int number1;
int number2;


and these numbers should not be written outside of the double loop, this brings me to the conclusion that they are not needed at all, and that you should write this:


        for (int i =0; i &lt; stack.Count; i++) {

            two_list[0] = stack[stackLast];

            two_list[1] = stack[i];

            result.Add(new int[] {two_list[0], two_list[1]});

        }



instead like this

for (int i =0; i &lt; stack.Count; i++) 
{
    result.Add(new int[] {stack[stackLast], stack[i]});
}