What did it do not working means nothing
that code just runs cool then hot for 3 sec

oh I posted my code below yours

 

Did you run the code i posted and if so what did it do ?

 

Did you run the code i posted and if so what did it do ?

I ran the code and the peltier plate was just hot, didn't turn cold at all

 

Thats a start
We need to find out some things to make this work

 

Try this part and see what it does

int i = 0;
void setup() {
  // TEC112703  controll pin initiate;
  pinMode(4, OUTPUT);
  pinMode(5, OUTPUT);
  pinMode(9, OUTPUT); // Speed control
  //Enable the Motor Shield output;
  pinMode(6, OUTPUT);
  digitalWrite(6, HIGH);
}
void loop() {
  digitalWrite(6, HIGH);
  digitalWrite(4, HIGH);
  digitalWrite(5, LOW);  // Set the current direction of TEC112703
  for (i = 20; i < 250; i = i + 5)
  {
    analogWrite(9, i);   // set the current of TEC112703

    delay(200);
  }
  Serial.println("stop 3s");
  digitalWrite(6, LOW);//Turns it all off
}

 

I ran the code and the peltier plate was just hot, didn't turn cold at all

Did you have a heat sink and fan on the hot side? Without removing all that heat, both sides will get hot.

 

It worked there site shows 2 ways to hook up motor the right way and the wrong one.
the motor goes on A1 and B1 looks like they lay it out A1 A2 which is showed on the first thing I found

But there sample code tells you to use D4 and D5 and D6 which is A1 and B1 motor hookup

Need to add some kind of pid to keep the temp where you would want it.