This is needlessly challenging.

var quizArray = [
  ["What is the name of earth's satellite? ", 'moon'],
  ["What color is grass? ", 'green'],
  ['German Shepherds are the best dogs: T/F ?', 'T']
];

let numCorrect = 0;

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

//this is to run the function itself. 
quizFunction();

//the quiz function holding all logic
function quizFunction() {

  let correctString = ""; //this is a string that will hold all the correct answers in LI tags.

  for (let i = 0; i < quizArray.length; i++) {
    var userPrompt = prompt(quizArray[i][0]);
    if (userPrompt === quizArray[i][1]) {
      numCorrect++;
      let isRight = quizArray[i][0];
      correctString += ("<li>" + isRight + "</li>"); //this adds the correct answer in LI tags to the string
    } // add else statement here
  } // ends for loop

  //I've put your print functions in the function so it only runs once per function, AFTER all the logic has been done
  print("You got " + numCorrect + " answers right." + "<br>");
  print("<h3>" + "You got these questions correct:" + "</h3>");
  print("<ol>" + correctString + "</ol>"); //this is where I put the string with all the correct answers in LI tags

} // ends function

// Creating an array of objects (list of objects).
// Question: is the question, obviously.
// Answer: is the correct answer,
// Given: is the answer given by user.
var qa = [
  {
    question: "What is the year I was born?", 
    answer: "1997",
    given: "",
  },
  {
    question: "What is my mother's first name?", 
    answer: "Jennifer",
    given: "",
  },
  {
    question: "What is my favorite color?", 
    answer: "Blue",
    given: "",
  },
  {
    question: "What is my favorite programming language?", 
    answer: "Javascript",
    given: "",
  },
];

// Array that will contain the answers that were correct
var correct = [];

// Array that will contain the answers that were not correct
var wrong   = [];

// ==
// = Asking the Question
// ==

// This for loop is running through every Object inside of the "qa" array.
for(var i = 0; i < qa.length; i++){

  // currentList is the current Object that is being looked at by the for loop.
  var currentList = qa[i];

  // Do While loops run at least once, and then run more if the condition is not met.
  do{
    // Prompt the user to answer the question, and assign it to the currentList's variable 'given'.
    currentList.given = prompt(currentList.question);

    // If the 'given' property is '' (blank), it will ask the question again.
  }while(currentList.given == "");
}

// At this point in the code, all the questions are answered, and all the 'given' properties in the 'qa' array have values.. Now time to check if the answers are correct.


// Once again, this for loop is running through every Object inside of the "qa" array.
for(var i = 0; i < qa.length; i++){

  // currentList is the current Object that is being looked at by the for loop.
  var currentList = qa[i];

  // Checking to see if the current object's answer property is equal to the given property.
  // You can use .toUpperCase() or .toLowerCase() on BOTH properties to make the script not case sensitive. Like I did below.
  if(currentList.answer.toUpperCase() == currentList.given.toUpperCase()){
    // If the answer and the given are the same, add it to the 'correct' array.
    correct.push(currentList);
  }else{
    // Else if the answer and the given are not the same, add it to the 'wrong' array.
    wrong.push(currentList);
  }
}

// Printing the amount of questions the user got correct
print("You got " + correct.length + " questions correct! <br><br>");

// Just some styling here by printing "Correct Answers:" as a title.
print("Correct answers: <br>");

// Run through all the correct answers, and print them to the page.
for(var i = 0; i < correct.length; i++){
  print((i + 1) + ". " + correct[i].question + " - Answer: " + correct[i].answer + "<br>");
}

// More styling.
print("Incorrect answers: <br>");

// Run through all the wrong answers, and print them to the page.
for(var i = 0; i < wrong.length; i++){
  print((i + 1) + ". " + wrong[i].question + " - Answer: " + wrong[i].answer + " - Your Answer: " + wrong[i].given + "<br>");
}

// Function to print the messages to the page.
function print(message) {
  document.write(message);
}