Look into C# Array.IndexOf approach and see how it works - a few issues to look into

LookIntoArrayIndexOf_Practice.cs

using System;
using System.Collections.Generic; 

class Solution
{
    public static int[] GetIndicesOfItemWeights(int[] arr, int limit)
    {
      // your code goes here
      if(arr == null || arr.Length == 0) 
      {
        return new int[0]; // empty array 
      }
      
      // assume that the array is not empty 
      var set = new HashSet<int>(); // O(n)
      
      var length = arr.Length; 
      for(int index = 0; index < length; index++)
      {
        var visit = arr[index]; // 4, 6, 10, 15
        var search = limit - visit; // 17, 15, 11, 6
        if(set.Contains(search)) // true
        {
          return new int[]{index, Array.LastIndexOf(arr, search)}; // 15, 6 [3, 1]
        }
        
        set.Add(visit); // 4, 6 , 10, 
      }
      
      return new int[0]; 
    }

    static void Main(string[] args)
    {
        var result = GetIndicesOfItemWeights(new int[]{4, 6, 10,15,16}, 21); 
        foreach(var item in result)
        {
          Console.WriteLine(item); 
        }
    }
}

// 3 - 15, 1 - 6, 15 + 6 = 21
// two items -> 
// sorted array -> O(nlogn)
// n(n-1) -> O(n^2)
// brute force 
// for(int first = 0; first < length - 1; first ++)
// for(int second = first + 1; second < length; second++)
//    sum = arr[first] + arr[second]
//    return new int[]{first, second}
// Array.Sort(arr) -> ascending order
// two pointers  4, 16 -> 20 < 21, -> 6 + 16 = 22, 6 + 15 
// O(n)   
// data search -> 
// extra -> 
// 4, 17 in hashset -> Dictionary<int, int>,  value, index
// <4, 0>, 
// 6 -> 15 , add <6, 1> to the table 
// when we find 4, 21-4 = 17. 
// Array.IndexOf(value) -> first occurrence -> hashtable -> hashset -> data search 

Things to look into:
Array.Sort -> I tried to write arr.Sort, so I need to look into Abstract class Array and the API Sort is defined.

Read c# Array -
Read 10 minutes - C# Arrays Tutorial
https://msdn.microsoft.com/en-us/library/aa288453(v=vs.71).aspx

20 minutes reading:
http://www.c-sharpcorner.com/article/working-with-arrays-in-C-Sharp/

Study stackoverflow posts related to C# Array -

More reading:
https://www.codeproject.com/Articles/6118/All-about-abstract-classes