The Program in C# Program to Count Specified Character (both cases) in Given String is given below:

using System;

namespace CharacterCounter
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine("Hello Codeauri Family,enter a string here to count the characters: ");
            string input = Console.ReadLine();
            Console.WriteLine("Well,enter the character you want to count: ");
            char character = Console.ReadLine()[0];
            
            // Convert the input to lowercase
            input = input.ToLower();
            
            // Count the specified character (both cases)
            int count = 0;
            foreach (char c in input)
            {
                if (c == character || c == char.ToUpper(character))
                {
                    count++;
                }
            }
            
            // Display the result
            Console.WriteLine("Okay, the character '" + character + "' appears " + count + " times in the input string.");
            Console.ReadKey();
        }
    }
}

Output:

Hello Codeauri Family,enter a string here to count the characters: twenty
Well,enter the character you want to count:
twenty
Okay, the character ‘t’ appears 2 times in the input string.

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Here are the step by step execution of above program:

1. The using System; statement imports the System namespace, which provides access to various basic and fundamental classes.
2. The namespace CharacterCounter declaration creates a new namespace with the name CharacterCounter.
3. The class Program declaration creates a new class with the name Program. This class contains the main entry point of the program.
4. The static void Main(string[] args) method is the entry point of the program. It’s called when the program starts.
5. The line Console.WriteLine("Hello Codeauri Family,enter a string here to count the characters: "); prints a message to the console, asking the user to enter a string.
6. The line string input = Console.ReadLine(); reads the input string from the user.
7. The line Console.WriteLine("Well,enter the character you want to count: "); prints a message to the console, asking the user to enter the character they want to count.
8. The line char character = Console.ReadLine()[0]; reads the input character from the user and stores it in the character variable. The [0] index accesses the first character of the input string.
9. The line input = input.ToLower(); converts the input string to lowercase using the ToLower method.
10. The foreach (char c in input) loop iterates through each character in the input string. The c variable stores the current character.
11. The line if (c == character || c == char.ToUpper(character)) checks if the current character is equal to the input character or its uppercase version. If this condition is true, the count variable is incremented.
12. The line Console.WriteLine("Okay, the character '" + character + "' appears " + count + " times in the input string."); displays the result of the character count.
13. The line Console.ReadKey(); waits for the user to press any key to exit the program.