Track mail to clients Create an application class named LetterDemo that instantiates objects
  of two classes named Letter and CertifiedLetter and that demonstrates
  all their methods. The classes are used by a company to keep track of
  the letter they mail to clients. The letter class includes
  auto-implemented properties for the name of the recipient and date
  mailed. Also , include a ToString() method that overrides the Object
  class's ToString() method and returns a string that contains the name
  of the class (using GetType()) and the Letter's data field values.
  Create a child class named CertifiedLetter that includes an auto
  implemented property that holds the tracking number for the letter.


using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using static System.Console;

namespace ConsoleApp16
{
class Program
{
    static void Main(string[] args)
    {


        Letter letter1 = new Letter();
        letter1.name = "\nSender: Justin";
        letter1.date = ("\nDate: March 4,2017 ");

        CertifiedLetter track = new CertifiedLetter();


        Write("Your letter has been recieved!");
        Write("\n");


        Write(letter1);
        Write("\n");
        Write("Tracking number:"+ track.GetHashCode());
        Write("\n");


    }
}
}



class Letter
{
public string name { get; set; }
public string date { get; set; }

public override string ToString()
{
    return (GetType() + ":" + this.name + "" + this.date);

}

}


class CertifiedLetter : Letter
{
    public string tracking { get; set; }

}


Looking to see how I could tighten up the code or if there is a better way to do this.
You fail to address the first sentence of your homework: you do not have an application class named LetterDemo.

I'm a strong believer in always specifying the access modifier.  Therefore both your Letter and CertifiedLetter classes should be decorated with public.

The name of your properties should be Pascal-cased.  Specifically they should begin with a capital letter, as in Name and Date.  I would suggest that Date is too generic a name, and that you should rename it to SentDate.  Why?  One day you may modify CertifiedLetter to record a ReceivedDateand having clearly named variables adds clarity to your code.

The Name property should only record the actual name, and ditch the preface.  You should omit forcing the user of your class to include "\nSender: ".

Likewise SentDate should omit "\nDate: " and only record the actual date.  Furthermore, the type for this property should be Date and not String.