You have used Y (week-based-year) instead of y (year-of-era). Learn the difference from the documentation and from answers to this question.

Simply create a LocalDate with the year, month and day and format it to a String using a DateTimeFormatter.

Demo:

import java.time.LocalDate;
import java.time.format.DateTimeFormatter;
import java.util.Locale;

public class Main {
    public static void main(String[] args) {
        int day = 12, month = 6, year = 2021;
        LocalDate date = LocalDate.of(year, month, day);
        DateTimeFormatter dtf = DateTimeFormatter.ofPattern("dd-MM-uuuu", Locale.ENGLISH);
        String formatted = dtf.format(date);
        System.out.println(formatted);
    }
}

Output:

2021-06-12

ONLINE DEMO

Here, you can use y instead of u but I prefer u to y.

Learn more about the modern Date-Time API from Trail: Date Time.

Note

A LocalDate is supposed to represent date units (year, month, day), and not a specific format. The default format used by LocalDate#toString is based on ISO 8601 standard. For a specific format, you need to format it into a String as shown above. It is like representing double d = 5.0 as the 5.000 which is done by formatting d into a String of this format.

public class Main {
    public static void main(String[] args) {
        double d = 5.0;
        NumberFormat formatter = new DecimalFormat("#0.000");
        String formatted = formatter.format(d);
        System.out.println(formatted);
    }
}

Output:

5.000

It could be short as:

LocalDate.now().format(DateTimeFormatter.ofPattern("dd/MM/yyyy"));

Just format the date while printing it out:

var date = LocalDate.now();
var locale = Locale.forLanguageTag("fa");
var formatter = DateTimeFormatter
        .ofPattern("d/MM/uuuu")
        .localizedBy(locale); // In Java 15+, this localizes the digits; you can comment it
var dateText = date.format(formatter);
var parsedDate = LocalDate.parse(dateText, formatter);

System.out.println("date: " + date);
System.out.println("Text format " + dateText);
System.out.println("parsedDate: " + parsedDate.format(formatter));