It works fine but seems much complex. 

I have changed code of MyClass.java file for this logic. 

public class SecondhighestSum {
    public static void main(String args[]) {

        int[] intArray = {24, 5, 3, 8, 9, 1, 6, 3, 12, 5, 9, 8, 12};
        int intHighestnumber = 0;
        int intSecondhighestnumber = 0;

        for (int intnumber = 0; intnumber < intArray.length - 1; intnumber++)
        {
            int num = intArray[intnumber] + intArray[intnumber + 1];
            if (intHighestnumber < num) {
                intSecondhighestnumber = intHighestnumber;
                intHighestnumber = num;
            } else {
                if (intSecondhighestnumber < num && num != intHighestnumber) {
                    intSecondhighestnumber = num;
                }
            }
        }
        System.out.println("SecondHighest Number   " + intSecondhighestnumber);
    }
}

Please test above code. 

-Amol

Scenario 2: 

Find out the second largest sum(sum of adjacent number) of unsorted array using single loop.

Consider below example: 

{5,3,4,2,1,6,8,7,1,2,6,4}

Array after sum of adjacent number is {8,7,6,3,7,14,15,8,3,8,10}

Second largest pair sum is 14.

Scenario 3:

Find out the pair of original numbers of second largest number of  this program.

Consider the second largest is 14, print the pair of 14 is { 8 , 6 }

Please Test the same and let me know 

-Master Oogway.