I'm complete lost with this assingment!!!!

Post some code.

First - this is homework, so the experts here are *forbidden* to do it for you.

I'm puzzled by your question as the details you give are the answer you want.
You have the nine digit number.
First digit.   1 is addition, 2 is subtraction, and 3 is multiplication. any other digit in this position is incorrect.  (You now have a valid or invalid number)
Now you know what you need to do to get the total (add, subtract, multiply).
You now have the total - is the right most digit the same as the rightmost in the code.  So you know if the code is valid or not.

this is the code that I did it , but my professor don't like it. he said is poor logic and code!!!! somebody can help me

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

#include <cctype> // for isdigit

using namespace std;

int main()
{
      int i; // auxiliar variable to check digit by digit
      int j; // stop to show results
      int baddata; // flag to identify if account is valid or invalid
      int totalsum; // total sum if operation is sum or substraction
      int totalmul; // total if operation is multiplication
      int totalcontrol; // variable used to truncate the total of control
      int finaltotal; // auxiliar variable to check the validity of the check// digit
      string accountno; // account number
      string message; // returned message
      cout << "Enter Account No" << '\n';
      cin >> accountno;
      message = "*** VALID ACCOUNT No ***";
      i=0;
      baddata = 0;
      totalsum = 0;
      totalmul = 1;
      totalcontrol = 0;
      finaltotal = 0;
      // check length of the account number
      if (accountno.length() != 9 )
      {
            message = "*** INVALID ACCOUNT No. ***";
            baddata = 1;
      }
      // check operation code
      if (baddata == 0)
      {
            if (accountno[0]=='1' || accountno[0]=='2' || accountno[0]=='3')
                  baddata = 0;
            else
            {
                  baddata = 1;
                  message = "***OPERATION CODE ERROR***";
            }
      }
      // check digit by digit and calculate total sum or total multiplication
      i = 0;
      if (baddata == 0)
      {
            do
            {
                  if (isdigit(accountno[i])==0)
                  {
                        message = "*** INVALID ACCOUNT No.***";
                        baddata = 1;
                        i = 10;
                  }
                  else
                  {
                        if (accountno[0]=='3')
                              totalmul = totalmul * (accountno[i]-'0');
                        else
                              totalsum = totalsum + (accountno[i]-'0');
                  }
                  i = i + 1;
            }while (i < 8);
      }
      // truncate the total sum or total multiplication to be able to validate the control digit
      if (baddata == 0)
      {
            if (totalsum > 0)
            totalcontrol = totalsum /10;
            else
                  totalcontrol = totalmul /10;
            
      }
      
      finaltotal = (totalcontrol * 10) + (accountno[8]-'0');
      if (baddata == 0)
      {
            if (finaltotal == totalmul || finaltotal == totalsum)
                  baddata = 0;
            else
                  message = "*** INVALID ACCOUNT CONTROL DIGIT ***";
      }
      cout << "Account No" << '\t' << accountno << '\t' << message << '\n';
      
      return 0;
}

Post some valid and invalid account numbers as an example.

use functions for example, rather than one big function.

if(NUMBER_FAILS_CHECK)
{
  PrintMessage("FAILED BECAUSE OF..");
  return 0;
}

You only require one totals variable.  Why do you need a separate one for multiplication?

I think my comments helped in solving the original question and I provided relevant comment to improve the code in response to the subsequent question.