"because when i make an object from that class this array changed each time" - you need to know about the static keyword in java.
Static Variables: In Java, variables can be declared with the static keyword. An example is given below. 
static int y = 0;
When a variable is declared with the keyword static, its called a class variable. All instances share the same copy of the variable. A class variable can be accessed directly with the class, without the need to create a instance.
Without the static keyword, it’s called instance variable, and each instance of the class has its own copy of the variable.
- It is a variable which belongs to the class and not to object(instance) 
- Static variables are initialized only once , at the start of the execution. These variables will be initialized first, before the initialization of any instance variables. 
- A single copy to be shared by all instances of the class. 
- A static variable can be accessed directly by the class name and doesn’t need any object 
Syntax : <class-name>.<variable-name>
Read the article on Static Methods, Variables, Static Block and Class with Example to know more in detail.
Edit: I wanted you to explore and solve it of your own but since you are struggling, i am adding a solution. Note that, you can achieve what you want in many ways.
class Game {
    private static final int max = 32;
    private static final int min = 1;
    private static final Integer[] words_Image = new Integer[10];
    static {
        setwords_Image();
    }
    private static void setwords_Image() {
        Random r = new Random();
        for (int i = 0; i < words_Image.length; i++) {
            int num = r.nextInt(max - min + 1) + min;
            int j = 0;
            while (j < i) {
                if (words_Image[j] == num) {
                    num = r.nextInt(max - min + 1) + min;
                    j = -1;
                }
                j += 1;
            }
            words_Image[i] = num;
        }
    }
    public Integer[] getWords_Image() {
        return words_Image;
    }
}
public class test {
    public static void main(String[] args) {
        Game g1 = new Game();
        System.out.println(Arrays.toString(g1.getWords_Image()));
        Game g2 = new Game();
        System.out.println(Arrays.toString(g2.getWords_Image()));
    }
}
It outputs: (as you expect)
[1, 32, 18, 20, 27, 8, 9, 31, 3, 19]
[1, 32, 18, 20, 27, 8, 9, 31, 3, 19]