Change Product Category Order

To change product categories order you can:

Use a shortcode to show categories

You can use the [show_categories] shortcode instead of the automatic listing, with the order and orderby attributes.

Please see the show categories shortcode docs for details. The Show Categories block has the same Order by and Order type settings.

Add a code to your theme functions.php

You will need the access to the FTP to achieve this. The best way to do it is using the child theme.

Find your theme functions.php file and place the following code to modify the product category listing order:

add_filter('show_categories_args','my_show_categories_args');
/**
* Modifies default product category order
*
* @param array $args
* @return array
**/
function my_show_categories_args($args) {
$args['orderby'] = 'id';
$args['order'] = 'ASC';
return $args;
}

This code will set the category order by ID - ascending. For the possible order and orderby values please see the show categories shortcode docs.
The code changes the order of the automatic category listings on the main catalog page and category pages, and of every [show_categories] shortcode. It doesn't apply when the Categories Display setting is set to URLs.