> However, I want to control six servos using the shield area circled in red below. Could anyone provide the code to setup and control servos from the area circled in red?

With the limited amount of info you have provided about the shield this will have to be a wild guess. I am assuming that the pins are S(ignal), V(cc) and G(nd) for pins 8-13. On an Arduino Mega these can be used for PWM and therefore Servo control. 

Include the Servo library, attach the pin and set the angle. 

    #include <Servo.h>

    Servo servo[6];   

    void setup() 
    {
      ...
      for (int i = 0; i < 6; i++)
        servo[i].attach(8 + i);
      ...
    }

    void loop() 
    {
       ...
       servo[i].write(pos);
       ...
    }

Cheers!

NB: Do not forget to provide the correct power supply. If USB Port is left, then the upper pin is positive and the lower pin negative.