Why is the access method not working?

Question

PHP

Hello!
This code should not allow the return to be set to less than 20, but any value can be set - a mess. How to fix?

<?php
class Car{
  public $age = 30;

  function __set($name, $value){
    if($value>20){ //Возвраст может быть только больше 20-и
      $this->$name = $value;
    }
  }
}
$car = new Car();
$car->age = 15; //Такого делать нельзя!
echo $car->age;
?>

Why is __set() a magic method? What is the name from? What is its feature?
There's a contradiction in the book I'm reading

Accessors do not apply to private properties.
The following statement will implicitly call the __set() function:
$a->attribute = 5;

Well, how will the __set() function be called if we access a public (public) property?
Nothing is clear. The documentation is also nonsense. Some magic methods...
Thanks in advance!