My counter won't go passed 1.. Any thoughts?

There is a mistake in your code, but to be fair to you it took me quite a bit to notice it. I even opened an IDE and played around and debugged the code because I was curious as I could not notice any obvious issues.

The problem stems from the fact that your if statement is placed after your for loop code block, in other words you run though the entire for loop (prompting for answers) before you check that the response and answer match, this means that only the last question will actually have it's answer checked. Which is why the maximum score you can get is 1.

Moving the if statement inside the for loop like this:

function print(message) {
  document.write(message);
}

var question;
var answer;
var response;
var rightAnswers = 0;
var html;


var questions = [
  ['How many letters are in my first name?', 4],
  ['What is my age?', 23],
  ['How old is my girlfriend', 24]
];

for (var i = 0; i < questions.length; i += 1) {
  question = questions[i][0];
  answer = questions[i][1];
  response = parseInt(prompt(question));
  if ( response === answer ) {
    rightAnswers += 1;
  } 
}

html = "You got " + rightAnswers + " question(s) right";
print(html);

Will fix the issue.