By default, all accommodation types are listed on the website by the date of publishing in a descending order. So the order throughout the website can be edited by changing the publishing date in the Accommodation tab > Accommodation Types > hover over an accommodation type > Quick Edit.
It is possible to change the order only in specific listings displayed with shortcodes. For example, this shortcode will display properties by their order number in an ascending order:
[mphb_rooms orderby="menu_order" order="ASC"]
The order number can be changed in the Accommodation tab > Accommodation Types > hover over an accommodation type > Quick Edit.
All the available ordering parameters are described in Accommodation > Shortcodes and in the plugin documentation.