2048 game moving tiles algorithm question

Hello everybody! I am looking for little help with my project. I have little problem with moving tiles algorithm in my version of 2048 game. It is very pre alpha code, I have a lot of work waiting for me in this project.

My game is storing every tile in GameObject[] table. I could get every tile by position [x,y] translated to index. Every tile have their own script with declared value.

How I could make this moving tile algorithm in proper way?

I found few source codes but I have problem with using it in my project.

I am sorry for polish variable names in project - I added few comments in English.

I think the idea of my code should be clear.

//here is my edited code of engineScript. - thanks Robert for comment!

 using UnityEngine;
 using System.Collections;
 
 public class engineScript : MonoBehaviour {
     public static int cols = 4; //maxX 
     public static int rows = 4; //maxY
     public static int minValue = 2, maxValue = 4;
     private int score = 0;
     private int currentTilesAmount;
     
     public Transform[,] tiles = new Transform[cols,rows];
     public GameObject tilePrefab;
     public float offset = 0.25f;
     
     // Use this for initialization
     void Start () {
         newTile();
         newTile();
     }
     
     // Update is called once per frame
     void Update () {
         if (Input.GetKeyDown(KeyCode.LeftArrow)){
             tilesLeft();
             newTile();
         }
         else
         if (Input.GetKeyDown(KeyCode.RightArrow)){
             tilesRight();
             newTile();
         }
         else
         if (Input.GetKeyDown(KeyCode.DownArrow)){
             tilesDown();
             newTile();
         }
         else
         if (Input.GetKeyDown(KeyCode.UpArrow)){
             tilesUp();
             newTile();
         }
         
     }
     
     void tilesLeft(){
 
     }
     void tilesRight(){
         
     }
     void tilesDown(){
         
     }
     void tilesUp(){
         
     }
     
     //generowanie losowej wartości startowej tiles - działa ok
     //generate random value for new tile
     int newTileValue(){
         int value;
         // find out if we are generating a tile with the lowest or highest value
         float highOrLowChance = Random.Range(0f, 0.99f);
         if (highOrLowChance <= 0.75f) {
             value = minValue;
         } else {
             value = maxValue;
         }
         return value;
     }
     
     //policz ile jest wolnych pozycji - działa OK
     //count of free positions in main table
     int freePositionAmount(){
         int freeSpace = 0, lockedSpace = 0;
         foreach(Transform t in tiles){
             if (t == null)
                 freeSpace++;
             else
                 lockedSpace++;
         }
         currentTilesAmount = lockedSpace;
 
         //number of free space
         Debug.Log("freePositionAmount: ilość wolnych miejsc w tablicy: " + freeSpace); //free space amount in table
         return freeSpace;
     }
     
     //losowanie wolnej pozycji w tablicy - działa OK
     //looking for free random position in table
     void randomFreePositon(out int posX, out int posY){
         //temporary variable for freePositionAmount
         int freeSpaceAmount = freePositionAmount();
 
         //tablica przechowująca wolne pozycje [x,y]
         //table with free position indexes [x,y]
         int[,] freePositions = new int[freeSpaceAmount,2];
         if(freeSpaceAmount > 0){
             int iterator = 0;
             for (int x = 0 ; x < cols ; x++)
                 for (int y = 0; y < rows; y++){
                     if (tiles[x,y] == null){
                     freePositions[iterator,0] = x; //free posX
                     freePositions[iterator,1] = y; //free posY
                     iterator++;
                     }
                 }
             
             //wybór randomowej pozycji w tablicy z wolnymi miejscami
             //select random free position in main table
             int random = Random.Range(0, freePositions.GetLength(0)-1);
             posX = freePositions[random,0];
             posY = freePositions[random,1];
         }
         else
         {
             Debug.Log("randomFreePosition: brak wolnych miejsc w tablicy!"); // there are no free space in table
             throw new UnityException("randomFreePosition: brak wolnych miejsc w tablicy!"); // there are no free space in table
         }
     }
     
     //tworzenie nowego obiektu tiles i dodanie do głównej tablicy kostek - działa OK
     //creating new tile and adding the object into main table
     void newTile(){
         //losowanie wolnej pozycji...
         //looking for free position...
         int x, y;
         randomFreePositon(out x, out y);
 
         //instantiate new tile at [x,y] position with offset
         GameObject tmp_tile = (GameObject) Instantiate(tilePrefab,new Vector3(x+(x*offset)-2,y + (y*offset)-2,0),Quaternion.identity);
 
         //add new tile to table
         if(tmp_tile){
             //przypisz losową wartość początkową 2 lub 4
             //random value for new tile
             tmp_tile.GetComponent<cubeScript>().value = newTileValue();
             
             //dodanie tiles do tablicy
             //add tile to table
             tiles[x,y] = tmp_tile.transform;
             Debug.Log("newTile: kostka została dodana do głównej tablicy!"); // new tile was succesfully added into main table
         }
     }
 }