How to display how many times an array element appears

You can handle this via Enumerable.GroupBy. I recommend looking at the C# LINQ samples section on Count and GroupBy for guidance.

In your case, this can be:

int[] values = new []{1,2,3,4,5,4,4,3};

var groups = values.GroupBy(v => v);
foreach(var group in groups)
    Console.WriteLine("Value {0} has {1} items", group.Key, group.Count());

You can keep a Dictionary of items found as well as their associated counts. In the example below, dict[d] refers to an element by its value. For example d = 4.

int[] List = new int[]{1,2,3,4,5,4,4,3};
var dict = new Dictionary<int, int>();
foreach(int d in List)
{
    if (dict.ContainsKey(d))
        dict[d]++;
    else
        dict.Add(d, 1);
}

When the foreach loop terminates you'll have one entry per unique value in dict. You can get the count of each item by accessing dict[d], where d is some integer value from your original list.

The LINQ answers are nice, but if you're trying to do it yourself:

int[] numberFound = new int[6];
int[] List = new int[] { 1, 2, 3, 4, 5, 4, 4, 3 };
foreach (int d in List)
{
    numberFound[d]++;
}