Nested for loop, not picking up first instance in Array

I am trying to encode a word, and I am not sure why my for loops aren't picking up the first instance, 0. The input for this method is "This" and 3. The output from this method is klv. So my loop must not be working properly as the letter T is getting skipped. What is wrong with my loops?

String encodeWord(String word, int Shift) {

        //word = "This"
		//Shift = 3, is how far the letter is shifted to the right of the original 
		char[] alphabet = "abcdefghijklmnopqrstuvwxyz".toCharArray();
		char[] temp = word.toCharArray();
		char[] FA = new char[temp.length];
		String tempWord = "";
		StringBuilder sb = new StringBuilder(64);


		

    for (int x = 0; x < word.length(); x++) {

			for (int y = 0; y < alphabet.length; y++) {
				if (word.charAt(0) == alphabet[y]) {
					FA[0] = alphabet[y + shift];
					System.out.println(FA[0]);
				}
			}
		}

		for (int i = 0; i < word.length(); i++) {

			for (int j = 0; j < alphabet.length; j++) {
				if (word.charAt(i) == alphabet[j]) {
					FA[i] = alphabet[j + shift];
					sb.append(FA[i]);
					System.out.println(FA[i]);
				}

			}
		}
		System.out.println(sb);

		return sb.toString();
	}

The letter 'T' is different from the letter 't', so since only the letter 't' is found in your array, the program won't find a match for the letter 'T'.

Another problem with your code is that you will get an Index out of bounds exception if the input contains the letters 'x', 'y' or 'z' because there aren't 3 letters after them in the array.

public static String encoder(String word, int shift)
{
	static const int max_char = 122; //letter 'z'
	static const int min_char = 97;  //letter 'a'
	char[] c_array = word.toCharArray();
	char[] encoded_string = new char[c_arary.length()];
	
	for(for i = 0; i < c_array.length(); i++)
	{
		if( ((int)c + shift) > max_char) //makes sure that the ascii isnt a non number
		{
		     encoded_string[i] = (min_char + (int)c + shift - max_char );  // this will correct the overflow 
		}
		
		c = c + shfit;
	}
	
	return encoded_string;
}

This is an easier way to do this... also your loops have a few logical errors.. the first one i caught was in the first loop... if there is a z in your word your going to overflow your alphabet array.

This is using the Ascii table way