how to create a parent and sub category in laravel 8 code example

Example: laravel parent child category

Calling the relationship function (->children()) will return an instance of the relation class. You either need to call then get() or just use the property:

$children = $category->children()->get();
// or
$children = $category->children;
Further explanation
Actually children() and children are something pretty different. children() just calls the method you defined for your relationship. The method returns an object of HasMany. You can use this to apply further query methods. For example:

$category->children()->orderBy('firstname')->get();
Now accessing the property children works differently. You never defined it, so Laravel does some magic in the background.

Let's have a look at Illuminate\Database\Eloquent\Model:

public function __get($key)
{
    return $this->getAttribute($key);
}
The __get function is called when you try to access a property on a PHP object that doesn't actually exist.

public function getAttribute($key)
{
    $inAttributes = array_key_exists($key, $this->attributes);

    // If the key references an attribute, we can just go ahead and return the
    // plain attribute value from the model. This allows every attribute to
    // be dynamically accessed through the _get method without accessors.
    if ($inAttributes || $this->hasGetMutator($key))
    {
        return $this->getAttributeValue($key);
    }

    // If the key already exists in the relationships array, it just means the
    // relationship has already been loaded, so we'll just return it out of
    // here because there is no need to query within the relations twice.
    if (array_key_exists($key, $this->relations))
    {
        return $this->relations[$key];
    }

    // If the "attribute" exists as a method on the model, we will just assume
    // it is a relationship and will load and return results from the query
    // and hydrate the relationship's value on the "relationships" array.
    $camelKey = camel_case($key);

    if (method_exists($this, $camelKey))
    {
        return $this->getRelationshipFromMethod($key, $camelKey);
    }
}
Then in getAttribute first is some code that checks for "normal" attributes and returns then. And finally, at the end of the method, if there's a relation method defined getRelationshipFromMethod is called.

It will then retrieve the result of the relationship and return that.