Your code was almost correct but there some mistakes

• You have to give the function a name
• You have to return count
• You have to pass actual strings
• You should use let or const instead of var
• You should use === instead of ==

function amount(word, letter) {
  let count = 0;
  for (let i = 0; i < word.length; i++) {
    if(word[i] === letter) count++
  }
  return count;
}

console.log(amount('door', 'o'));

Using array methods you can simplify even more

function amount(word, letter) {
  return Array.prototype.reduce.call(word, (acc, el) => acc + (el === letter), 0);
}

console.log(amount('door', 'o'));

You can split the string into an array, then loop through each of the letters. We have a letterTracker object, which is where our values are stored. If the key of the letter doesn't exist in the object already, we'll add the key to it. If it does exist, we'll just add one to it.

var countLetters = (string)=>{
    const stringArr = string.split('')
    let letterTracker = {};
    stringArr.forEach(letter=>{
        letterTracker[letter]
            ? letterTracker[letter]++
            : letterTracker[letter] = 1
    });
    return letterTracker;
}

countLetters('wuddup'); //returns { w: 1, u: 2, d: 2, p: 1 }

Using a more ES5 friendly method, and without splitting the string into an array, we can do this (the same result will be achieved):

function countLetters(string){
    let letterTracker = {};
    for(let i = 0; i < string.length; i++){
        if(letterTracker[string[i]]){
            letterTracker[string[i]]++
        } else {
            letterTracker[string[i]] = 1
        }
    }
    return letterTracker;
}

countLetters('wuddupp?'); //returns { w: 1, u: 2, d: 2, p: 2, ?: 1 }