You can use Map here to achieve the result:

let colors = [
  ["blue", "green", 5.0, 57],
  ["blue", "green", 5.0, 57],
  ["yellow", "green", 8.3, 84],
  ["blue", "green", 5.0, 57],
  ["orange", "blue", 7.0, 0],
  ["yellow", "green", 8.3, 84],
];

function count_duplicate() {
  let counts = new Map();

  for (let i = 0; i < colors.length; i++) {
    const data = counts.get(colors[i].toString());
    if (data) data.count++;
    else counts.set(colors[i].toString(), { value: colors[i], count: 1 });
  }

  const result = [];
  for (let [, { value, count }] of counts) {
    result.push([...value, count]);
  }
  return result;
}

console.log(count_duplicate());

change from array [] to an object {}, to easly manipulate each sub-array(row) how many times occures, it should be an object not an array! and Using Object.entries looping through its key(str) and value(times), and return str splitted by comma and their times of occurences.

let colors = [
  ["blue", "green", 5.0, 57],
  ["blue", "green", 5.0, 57],
  ["yellow", "green", 8.3, 84],
  ["blue", "green", 5.0, 57],
  ["orange", "blue", 7.0, 0],
  ["yellow", "green", 8.3, 84],
];

function count_duplicate() {
  let counts = {};//<-- 
  for (let i = 0; i < colors.length; i++) {
    if (counts[colors[i]]) {
      counts[colors[i]] += 1;
    } else {
      counts[colors[i]] = 1;
    }
  }
 console.log(counts); //{ 'blue,green,5,57': 3, 'yellow,green,8.3,84': 2, 'orange,blue,7,0': 1 }
  const res = Object.entries(counts).map((count) => {
    [str, times] = count; //['blue,green,5,57': 3]
    return [...str.split(","), times];//[ 'blue', 'green', '5', '57', 3 ]
  });
  console.log(res);
}
count_duplicate();

Result:

[ [ 'blue', 'green', '5', '57', 3 ],
  [ 'yellow', 'green', '8.3', '84', 2 ],
  [ 'orange', 'blue', '7', '0', 1 ] ]

I don't know about fancy syntax but using a hashmap should work which is just a JavaScript object.

let colors = [
        ['blue', 'green', 5.00, 57],
        ['blue', 'green', 5.00, 57],
        ['yellow', 'green', 8.30, 84],
        ['blue', 'green', 5.00, 57],
        ['orange', 'blue', 7.00, 0],
        ['yellow', 'green', 8.30, 84],
       
];

const hashmap = {};

colors.forEach(color => {
    const key = JSON.stringify(color);
    if(!hashmap[key]) hashmap[key] = 1;
    else hashmap[key]++;
    if(hashmap[key] == 1) return color;
});

console.log(hashmap);

const uniqueArray = [];

for(const key in hashmap) 
    uniqueArray.push(JSON.parse(key));

console.log(uniqueArray);