Can Anyone Help Me Understand What I am Doing Wrong?

There are two things wrong here.

  1. This is not the way to check if a variable has a value between two values. You will have to do two compares; e.g.
while (4000 < ttt && ttt < 11000);
// && is a logical AND; you can also use the keyword 'AND'
  1. The semicolon ends the while-loop so whatever is after that will be executed unconditionally (the same affect as if you did not have the while condition).
  1. Often beginners assume that this means that ttt will follow millis(); not sure if that is the case for you but you will have to refresh ttt ever so often so it reflects the actual millis().
  2. You should not call functions that rely on hardware in the global declaration section of the program; millis() might not work as expected and if ttt gets a value between 4000 and 11000, you will enter the while-loop but you will never get out of it because you don't update ttt.
    If you don't assign a value, you're program will kind-of do what you expect.
//unsigned long ttt = millis();
unsigned long ttt;

That might very well be the bootloader kicking in after a reset of the board; though I would expect two or three flashes.

To fix your problem, assign millis() to ttt in the beginning of loop() and replace the while loop by an if statement The below code will flash your leds in the period from 4 seconds after reset till 11 seconds after reset.

void loop()
{
  // get the current time
  ttt = millis();
  
  if (4000 < ttt  && ttt < 11000)
  {
    digitalWrite(11, HIGH); // sets the digital pin 11 on
    delay(100); // waits for a second
    digitalWrite(11, LOW); // sets the digital pin 11 off
    delay(100); // waits for a second

    digitalWrite(12, HIGH); // sets the digital pin 12 on
    delay(100); // waits for a second
    digitalWrite(12, LOW); // sets the digital pin 12 off
    delay(100); // waits for a second

    digitalWrite(13, HIGH); // sets the digital pin 13 on
    delay(100); // waits for a second
    digitalWrite(13, LOW); // sets the digital pin 13 off
    delay(100); // waits for a second
  }
}

You can ignore point (4) when using above code.

One last comment: mixing millis() and delay() is often not going to give the desired results.