Solution to the challenge.

let search;
let message = "";
// We dont need "let namesNotFound = [];" anymore

function print(message) {
  let output = document.getElementById("output");
  output.innerHTML = message;
}

while (true) {
  search = prompt(
    'please enter a student name to search for or type "quit" to exit'
  );
  search = search.toLowerCase();
  if (search === null || search === "quit") {
    break;
  }
  // We don't need "let notfoundCounter= 0;" here anymore either
  for (let index = 0; index < students.length; index++) {
    const student = students[index];
    if (search === student.name.toLowerCase()) {
      message += `<h2>student Name: ${student.name}</h2>
                 <p>student Track: ${student.track}</p>
                 <p>student Achievements: ${student.achievements}</p>
                 <p>student Points: ${student.points}</p>`;
      print(message);
    } else if (message === "") {
      print(
        `<h2>Student ${search} is not in our database, Please try again.</h2>`
      );
    }
  }
  message = ``; // This makes 'let message' go back to empty "" value every time the loops end so it doesn't print previous search results over and over again.
}

// function which is aiming "notFound Output in your HTML file is not here anymore aswell so you don't need "notFound Output" ID in your HTML file anymore.

let students = [
  { name: "Greg", track: "Web design, CSS", achievments: 763, points: 122 },
  { name: "Adam", track: "Web design", achievments: 163, points: 422 },
  { name: "Tom", track: "CSS", achievments: 653, points: 152 },
  { name: "Martin", track: "Web design, JS", achievments: 713, points: 162 },
  { name: "Ben", track: "JS, CSS", achievments: 773, points: 1127 },
  { name: "Josh", track: "JS, CSS", achievments: 773, points: 1127 },
  { name: "Tad", track: "JS, CSS", achievments: 773, points: 1127 },
  { name: "Greg", track: "JS, CSS", achievments: 1254, points: 1112 },
  { name: "Anna", track: "JS, CSS", achievments: 1254, points: 1112 },
  { name: "Tim", track: "JS, CSS", achievments: 1254, points: 1112 },
];

let message = "Type in a name of student you are looking for.";
message += ' If you wish to see all the names of our stundents type"list".';
message += ' If you wish to quit our program type "quit".';
let html;
let search;
let fulList;

// functions

function print(message) {
  var outputDiv = document.getElementById("output");
  outputDiv.innerHTML = message;
}

function list(number) {
  let position = `<li style="font-size:22px">${capitalizeFirstLetter(
    students[number].name
  )}</li>`;
  return position;
}

function capitalizeFirstLetter(string) {
  return string.charAt(0).toUpperCase() + string.slice(1);
}

function printInformation(number) {
  let print = `<h2>Student: ${students[number].name}</h2>`;
  print += `<p>Track: ${students[number].track}</p>`;
  print += `<p>Achievments: ${students[number].achievments}</p>`;
  print += `<p>Points: ${students[number].points}</p>`;
  return print;
}

// loops

while (true) {
  search = prompt(message);
  search = search.toLowerCase();
  fulList = "<h2>List</h2><ol>";
  html = " ";

  if (search === "quit" || search === 'null') {
    print("<h1>End</h2>.");
    break;
  }

  for (let i = 0; i < students.length; i += 1) {
    if (search === "list") {
      fulList += `${list(i)}`;
      html = fulList;
    } else if (search === students[i].name.toLowerCase()) {
      html += `${printInformation(i)}`;
    }
  }

  if (html === " ") {
    html = `<h2>Student ${capitalizeFirstLetter(
      search
    )} is not in our base, sorry. Try again.</h2>`;
  }

  print(html);
}

var student;
var search;
var outputMsge='';
function printToPage(message){
var div = document.querySelector('#output');
  div.innerHTML =message;
}
function studentReport(student){
    var report = `<h2>student: ${student.name}</h2>`;
      report+=`<p>track: ${student.track}</p>`;
      report+=`<p>achievements: ${student.achievements}</p>`;
      report+=`<p>points: ${student.points}</p>`;
      return report;
}
while(true){
search = prompt(`type your name to get report or type quit to exit the page`);
  if(search === null || search.toLowerCase() === 'quit'){
    break;
  } 
} // this curly brace here ends your "while infinite" loop, which makes your JS run over and over again through ONLY this part of script, and not going further to next part underneath.  

for(i=0; i< students.length; i+=1){
  student=students[i];
    if(search === student.name){
      outputMsge = studentReport(student);
      printToPage(outputMsge);
    }
  }

var student;
var search;
var outputMsge = "";
function printToPage(message) {
  var div = document.querySelector("#output");
  div.innerHTML = message;
}

function studentReport(student) {
  var report = `<h2>student: ${student.name}</h2>`;
  report += `<p>track: ${student.track}</p>`;
  report += `<p>achievements: ${student.achievements}</p>`;
  report += `<p>points: ${student.points}</p>`;
  return report;
}

while (true) {
  search = prompt(`type your name to get report or type quit to exit the page`);

  if (search === null || search.toLowerCase() === "quit") {
    break;
  }
 // I removed curly brace here
  for (i = 0; i < students.length; i += 1) {
    search = search.toLowerCase();
    student = students[i];
    if (search === student.name.toLowerCase) {
      outputMsge = studentReport(student);
      printToPage(outputMsge);
    }
  }
} // and I've added it here