PHP：在类中访问私有变量

I've been doing a project in PHP for the last few hours and I have encountered into a problem.

The problem is I don't know how to access private variables in a class and I can't find it online.

Example:

<?php
    class Example{
        private $age;

        public function __construct() {
            $age = 14;
            $this->checkAge();
        }
        private function checkAge() {
            if($this->$age > 12)
                echo "welcome!";
        }
    }
    $boy = new Example();
?>

As far as I know, I should be able to access the variable with $this->$age but it isn't working.

Thank you.

EDIT: Got it working with help of the awesome stackoverflooooooooow community, this is how a working one looks.

<?php
    class Example{
        private $age;

        public function __construct() {
            $this->age = 14;
            $this->checkAge();
        }
        private function checkAge() {
            if($this->age > 12)
                echo "welcome!";
        }
    }
    $boy = new Example();
?>

Look at this approach.
first: create Entity that stores and retrieves data inside of private $attributes array, and with magic __set(), __get() You can also do like: $object->variable = 123

second: extend Entity with Human class and add some function specific to child class (for example hasValidAge()):

<?php
    class Entity {
        private $attributes;

        public function __construct($attributes = []) {
            $this->setAttributes($attributes);
        }

        public function setAttribute($key, $value) {
            $this->attributes[$key] = $value;
            return $this;
        }

        public function setAttributes($attributes = []) {
            foreach($attributes AS $key => $value) {
              $this->setAttribute($key, $value);
            }
        }

        public function getAttribute($key, $fallback = null) {
            return (isset($this->attributes[$key]))? 
                   $this->attributes[$key] : $fallback;
        }

        public function __get($key) {
            return $this->getAttribute($key);
        }

        public function __set($key, $value) {
            $this->setAttribute($key, $value);
        }
    }

    class Human extends Entity {
        public function __construct($attributes = []) {
            $this->setAttributes($attributes);
            $this->checkAge();
        }

        public function hasValidAge() {
            return ($this->getAttribute('age') > 12)? true : false;
        }
    }

    $boy = new Human(['name' => 'Mark', 'age' => 14]);
    if($boy->hasValidAge()) {
        echo "Welcome ".$boy->name."!";
    }

?>

p.s. I've removed echo "Welcome!" part from constructor because it's not cool to do echo from model object, in our example Human is model of Entity.