How to add several string together such as "123"+"456"?

The expression "2323" is not a std::string, it is a const char[5].

Since C++14, you can have a literal of type std::string:

using namespace std::string_literals;

std::string a = "2323"s + "22323"s + "232332"s;

In this declaration

std::string a="2323" + "22323" + "232332";

you are using an expression with string literals and the operator + that is not defined for character arrays and correspondingly for pointers to which the string literals are implicitly converted.

You could write for example

std::string a = "2323"s + "22323" + "232332";

using the user-defined string literal "2323"s or you could write

std::string a = std::string( "2323" ) + "22323" + "232332";

Another way is to declare the object a like

std::string a;

and then write

a += "2323";
a += "22323";
a += "232332";

Here is a demonstrative program.

#include <iostream>
#include <string>

int main() 
{
    {
        using namespace std::literals;
        
        std::string a = "2323"s + "22323" + "232332";
        std::cout << a << '\n';
    }
    
    {
        std::string a = std::string( "2323" ) + "22323" + "232332";
        std::cout << a << '\n';
    }
    
    {
        std::string a;
        
        a += "2323";
        a += "22323";
        a += "232332";
        
        std::cout << a << '\n';
    }
    
    return 0;
}

The program output is

232322323232332
232322323232332
232322323232332

There is no predefined operator+ for const char[X] (a const array of char, with X the number of characters in it; e.g. const char[5] is the type of a literal "2323" as in your code) - nor for const char *, to which they could be automatically converted. That's why C++ compilers will not let you do this. However, there is an operator+ for std::string. Since this operator in turn returns a string, you can chain-call, that is, call the + operator again on its result. So you can write something like this:

std::string a = std::string("2323") + "22323" + "232332";

In case you are already using C++14 or later, you can use literals of type string via an s suffix, then an alternate form of writing this would be

using namespace std::string_literals;
std::string a = "2323"s + "22323" + "232332";

If it is just multiple const char[X] literals that you want to concatenate, you can also just write them one after the other, like this:

std::string a("2323" "22323" "232332");
// or:
std::string a = "2323" "22323" "232332";

The compiler will automatically concatenate them for you.

In addition to the other answers provided, you can also use the std::stringstream to build up an std::string.

#include <sstream>

int main( )
{
    std::stringstream ss{ };
    ss << "2323" << "22323" << "232332";

   // Maybe you also want to conditionally append something else.
   if ( some_condition )
   {
       // Note that I'm inserting an integer here.
       ss << 42;
   }

   // When you're ready you can call the str( ) member function
   // to attain a copy of the underlying string.
   std::string s{ ss.str( ) };
}