How to add score after destroying object?

Before this, I have made a scoring section to my program that used Invoke repeating every 1s. Now, I have problem how to make my scoring counter add an additional score when I destroy some objects.

using UnityEngine;
using System.Collections;
using UnityEngine.UI;

public class UIManager : MonoBehaviour
{

    public Button[] buttons;
    public Button pauseButton;
    public Image[] images;
    public Text scoreText;
    public Text highScoreText;
    public Text yourScoreText;
    public Text text;
    bool gameOver;
    int score;
    levelscroller level;
    CoinMove cm;
    void Start()
    {
        gameOver = false;
        score = 0 + cm.plus;
        InvokeRepeating("scoreUpdate", 1.0f, 1.0f);
    }
    void Update()
    {
        storeHighScore(score);
        scoreText.text = "" + score;
        yourScoreText.text = "" + score;
        highScoreText.text = "" + PlayerPrefs.GetInt("highscore");
    }
    void scoreUpdate()
    {
        if (gameOver == false)
        {
            score += 1;
        }
    }
    void storeHighScore(int newHighscore)
    {
        int oldHighscore = PlayerPrefs.GetInt("highscore", 0);
        if (newHighscore > oldHighscore)
        {
            PlayerPrefs.SetInt("highscore", newHighscore);
            oldHighscore = newHighscore;
            PlayerPrefs.Save();
        }
    }

Another class:

using UnityEngine;
using System.Collections;
public class CoinMove : MonoBehaviour
{
    public float Speed;
    public int plus = 0;
    UIManager ui;
    void Start()
    {

    }
    void Update()
    {
        transform.Translate(new Vector3(0, -1, 0) * Speed * Time.deltaTime);
        //if (Input.touchCount > 0 || Input.GetTouch(0).phase == TouchPhase.Began)
        //{
        //    Destroy(transform.gameObject);  
        //}
    }
    private void OnMouseDown()
    {
        Destroy(gameObject);
        plus += 10;
    }
}

It just make the counter of score totally 0.

You need a reference on the CoinMove script of the UIManager, then you need to make the score field public and access it from the CoinMove and add to it whatever you want. Anyway took the liberty to optimize your code a bit here:

public class UIManager : MonoBehaviour
{

    public Button[] buttons;
    public Button pauseButton;
    public Image[] images;
    public Text scoreText;
    public Text highScoreText;
    public Text yourScoreText;
    public Text text;
    bool gameOver;
    public int score;
    int initialScore;
    int oldHighScore;
    WaitForSeconds wfs;
    levelscroller level;
    string scoreString;
    void Start()
    {
        initialScore = score;
        oldHighScore = PlayerPrefs.GetInt("highscore", 0);
        highScoreText.text = oldHighScore.ToString();
        wfs = new WaitForSeconds(1f);
        gameOver = false;
        StartCoroutine(ScoreUpdate());
    }
    void Update()
    {
        if (gameOver)
            storeHighScore();

        if (score != initialScore)
        {
            scoreString = "" + score.ToString();
            scoreText.text = scoreString;
            yourScoreText.text = scoreString;
            if (score> oldHighScore)
            {
                highScoreText.text = scoreString;
            }
            initialScore = score;
        }

    }
    IEnumerator ScoreUpdate()
    {
        while (!gameOver)
        {
            score += 1;
            yield return wfs;
        }
    }
    
    void storeHighScore()
    {
        if (score > oldHighScore)
        {
            PlayerPrefs.SetInt("highscore", score);
            PlayerPrefs.Save();
        }
    }
}
public class CoinMove : MonoBehaviour
{
    public float Speed;
    public int bonus = 10;
    UIManager ui;
    public UIManager uiManager;     //set the reference in the Editor
    
    void Update()
    {
        transform.Translate(new Vector3(0, -1, 0) * Speed * Time.deltaTime);
        //if (Input.touchCount > 0 || Input.GetTouch(0).phase == TouchPhase.Began)
        //{
        //    Destroy(transform.gameObject);  
        //}
    }
    private void OnMouseDown()
    {
        uiManager.score += bonus;
        Destroy(gameObject);
    }
}

Cheers, hope that helps.
Note1: if you don’t want to change your code that much just make the score field public, copy the CoinMove class and set the reference of the UIManager in each instance of the CoinMove and it should work.

Note2: the constant accessing of the registry is not good you only need to save the highscore once the game is over not on every frame.

Note3: it might have some errors didn’t test it but you should get the logic behind it.