Javascript code sample. Disclaimer: This algorithem is not the best and optimised.

passwordGenerator.js

/*
 * Password Generator
 *
 * @author Shaun Thomas
 *
 * Objective
 * --
 *  \_ Generate 12 character length password from domain name
 *  \_ Re-creatable by hand without much complexity
 *  \_ Password has decent level of randomness
 */

console.log("*\n* Password Generator \n*");

/*
 * Step 1: Enter domain name
 */
var domainName = "google";

/*
 * Step 2: Take first 7 characters (customizable) of the domain name.
 * If the domain has less characters then append 0’s
 */
var DOMAIN_NAME_LENGTH_TO_CONSIDER = 7;

var password;
if(domainName.length >= DOMAIN_NAME_LENGTH_TO_CONSIDER) {
  password = domainName.substr(0, DOMAIN_NAME_LENGTH_TO_CONSIDER);
}
else {
  password = domainName;
  while(password.length < DOMAIN_NAME_LENGTH_TO_CONSIDER) {
    password = password.concat("0");
  }
}
console.log("First password phrase: "+ password);

/*
 * Step 3: Choose a 3 digit random number (Remember this random number. Can be used across different domains)
 */
var firstRandomNumberValue = 152;
var firstRandomNumber = firstRandomNumberValue.toString();

/*
 * Step 4: Insert the above random number into the first password phrase at positions 3, 5 and 7
 */
var numberInsertPositions = [3, 5, 7];
for(var idx=0 ; idx < numberInsertPositions.length ; idx++) {
  var pwArray = [];
  pwArray[0] = password.slice(0, numberInsertPositions[idx] - 1);
  pwArray[0] = pwArray[0].concat(firstRandomNumber.charAt(idx));

  pwArray[1] = password.slice(numberInsertPositions[idx] - 1);
  password = pwArray.join('');
}
console.log("Second password phrase: "+ password);

/*
 * Step 5: Choose another 3 digit random number (Remember this random number. Can be used across different domains)
 */
var secondRandomNumberValue = 765;
var secondRandomNumber = secondRandomNumberValue.toString();

/*
 * Step 6: Add the digits (from left to right) in the random number above with the character code of characters at
 * position 2, 4 and 6 of the second password phrase
 */
var characterIncrementPositions = [2, 4, 6];
for(var idx = 0; idx < characterIncrementPositions.length ; idx++) {
  var characterIncrementIndex = characterIncrementPositions[idx] - 1;
  var characterToIncrement = password.charAt(characterIncrementIndex);

  var characterToInsert;
  // If the character is 0 just consider the digit to insert
  if(characterToIncrement === "0") {
    characterToInsert = secondRandomNumber.charAt(idx)
  }
  else {
    var charCodeOfNewCharToInsert = characterToIncrement.charCodeAt(0) + parseInt(secondRandomNumber.charAt(idx));
    // If charCodeOfNewCharToInsert is greater than the range of English letters then start again from 'a' after 'z'
    if(charCodeOfNewCharToInsert - 97 > 26) {
      charCodeOfNewCharToInsert -= 26;
    }
    characterToInsert = String.fromCharCode(charCodeOfNewCharToInsert);
  }
  password = [ password.slice(0, characterIncrementIndex),
              characterToInsert,
              password.slice(characterIncrementIndex + 1)].join('');
}
console.log("Third password phrase: "+ password);

/*
 * Step 7: Prepend four special characters to the third password phrase to make the password
 */
var specialCharactersToPrepend = "$#+!";
password = specialCharactersToPrepend + password;
console.log("*\n* Final password: "+ password + "\n*");