I have a multi-dimensional array that looks like this: The base array is indexed based on category ids from my catalog.
$cat[category_id]
Ea
First you create an empty array, it will be used to store your result.
$result = array();
You need to iterate through your initial array, you can use foreach().
Then, given your parent_category_id simply use an if statement to check whether it's the given id or not.
If it is, just construct and push your result to your $result array.
Use any of the sort functions you like
Use the magic return $result;
You're done.