my solution

int sum[] = new int[16];
    int h = 0;
    for (int i = 0; i < 4; i++) {
        for (int j = 0; j < 4; j++) {
            sum[h] = arr[i][j] + arr[i][j+1] + arr[i][j+2]
                    + arr[i+1][j+1] + arr[i+2][j] + arr[i+2][j+1]
                    + arr[i+2][j+2];
            h++;
        }
    }
    Arrays.sort(sum);
    System.out.println(sum[15]);