for (int counter = 0; counter > size ; counter ++ )
     {


        sum = sum + score[counter];


       }
        average =  sum /size;
        cout << "The average Score is:" << average << endl;

}
void sortData(string* name, int* score, int size)
{

     int index_one, index_two;

      char temp;

   for ( index_one = 0; index_one < (size - 1); index_one++)
   {
      for(int index_two = index_one + 1; index_two < size; index_two++)
      {



         if (name  [index_one] > name [ index_two])
         {
            temp = name [ index_one];
            name [index_one] = name [index_two];
            name [index_two] = temp;


            temp = score [index_one];
            score [index_one] = score [index_two];
            score [index_two] = temp;


         }
      }
   }
}
 void displayData (string *name , int *score, int size)
 {
    cout << "Name \t\t Score\n";

    cout << "---------------------------------";

     for (int index = 0; index > size ; index++)
      {

         cout << name [index] << "\t";
         cout << setw(14) << score [index] << endl;

      }
}
#include<iostream>
#include<string>
#include<iomanip>

   using namespace std;

//function prototype



   void sortData(string* ,int*);
   void calcAverage(int*, int);
   void displayData(string* , int*, int);

     int main ()
   {

   // pointer variables
      string* name;

      int *score;
      int size;
      int counter;

   //dynamic variables



   // user enter score

      cout<<"How many test scores will you enter?";

      cin >> size;
      score = new int[size];
      name = new string [size];


      for(counter = 0; counter< size; counter ++)
      {
         cout<< "Enter students last name ";

         cin >> *(name  + counter) ;

         cout << " Enter the student's test score: ";

         cin >> * (score + counter);
      }


   }
     // function to calculate Average

    void calcAverage(int* score, int size)
   {
      int sum = 0;

      float average;
      for (int counter = 0; counter > size ; counter ++ )
      {


         sum = sum + score[counter];


      }
      average =  sum /size;
      cout << "The average Score is:" << average << endl;

   }

     // function to sort student name with the test score respectively.

     void sortData(string* name, int* score, int size)
   {

      int index_one, index_two;

      char temp;

      for ( index_one = 0; index_one < (size - 1); index_one++)
      {
         for(int index_two = index_one + 1; index_two < size; index_two++)
         {



            if (name  [index_one] > name [ index_two])
            {
               temp = name [ index_one];
               name [index_one] = name [index_two];
               name [index_two] = temp;


               temp = score [index_one];
               score [index_one] = score [index_two];
               score [index_two] = temp;


            }
         }
      }
   }
    void displayData (string *name , int *score, int size)
   {
      cout << "Name \t\t Score\n";

      cout << "---------------------------------";

      for (int index = 0; index > size ; index++)
      {

         cout << name [index] << "\t";
         cout << setw(14) << score [index] << endl;

      }
   }

Could you indicate which line is 89.

for (int index = 0; index > size ; index++)

This could be your issue.
Please use code tags, you will get more help.
For this to run size would have to have a negative value and as you increment index it will always be larger, so infinite loop.

#include<iostream>
#include<string>
#include<iomanip>

   using namespace std;

//function prototype



   void sortData(string* ,int*);
   void calcAverage(int*, int);
   void displayData(string* , int*, int);
   
	 int main ()
   {
   
   // pointer variables
      string* name;
   
      int *score;
      int size;
      int counter;
   
   //dynamic variables
   
   
   
   // user enter score
   
      cout<<"How many test scores will you enter?";
   
      cin >> size;
      score = new int[size];
      name = new string [size];
   
   
      for(counter = 0; counter< size; counter ++)
      {
         cout<< "Enter students last name ";
      
         cin >> *(name  + counter) ;
      
         cout << " Enter the student's test score: ";
      
         cin >> * (score + counter);
      }
   
   
   }
     // function to calculate Average
	  
    void calcAverage(int* score, int size)
   {
      int sum = 0;
   
      float average;
      for (int counter = 0; counter > size ; counter ++ )
      {
      
      
         sum = sum + score[counter];
      
      
      }
      average =  sum /size;
      cout << "The average Score is:" << average << endl;
   
   }
    
	 // function to sort student name with the test score respectively.
	 
	 void sortData(string* name, int* score, int size)
   {
   
      int index_one, index_two;
   
      char temp;
   
      for ( index_one = 0; index_one < (size - 1); index_one++)
      {
         for(int index_two = index_one + 1; index_two < size; index_two++)
         {
         
         
         
            if (name  [index_one] > name [ index_two])
            {
               temp = name [ index_one];
               name [index_one] = name [index_two];
               name [index_two] = temp;
            
            
               temp = score [index_one];
               score [index_one] = score [index_two];
               score [index_two] = temp;
            
            
            }
         }
      }
   }
    void displayData (string *name , int *score, int size)
   {
      cout << "Name \t\t Score\n";
   
      cout << "---------------------------------";
   
      for (int index = 0; index > size ; index++)
      {
      
         cout << name [index] << "\t";
         cout << setw(14) << score [index] << endl;
      
      }
   }

Line 89 is " temp = name [ index_one]; "

Error is
D:\Workspaces\CodeBlocks\Test\main.cpp|89|error: cannot convert `std::basic_string<char, std::char_traits<char>, std::allocator<char> >' to `char' in assignment|

deref of string* returns string and deref of int* returns int. You're trying to assign a string to a char on line 89. That's the problem.
(PS: Same problem exists 6 lines below where you try to assign int to char. Unfortunately it might work! Fix it.

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