Here are some quick instructions to install Wordpress on a MoodleBox. This is given absolutely without any support: you're on your own on this one, be warned!

Create a database for your WordPress on the MoodleBox. You can do this easily by visiting http://moodlebox.home/adminer.php (see: https://moodlebox.net/en/help/access-to-the-database-management-interface/) and clicking Create database. A good database name would be wordpress
Access to the MoodleBox via SSH (see: https://moodlebox.net/en/help/command-line-connection/)
Change the working directory to /var/www/: cd /var/www/
Download Wordpress, using e.g. sudo wget -c https://wordpress.org/latest.tar.gz and expand it with sudo tar -xzf latest.tar.gz
Change owner and group of wordpress folder: sudo chown -R www-data:www-data wordpress/
Delete downloaded compressed file to save some place: sudo rm latest.tar.gz (optional)
Create a soft link to the Wordpress installation: sudo ln -s /var/www/wordpress/ /var/www/moodle/wordpress
With your browser, access the URL: http://moodlebox.home/wordpress/ and finish the installation, using the correct infos:
- database name: whatever you enter at the first step, e.g. wordpress
- database username: moodlebox
- database password: MoodleBox4$ (or what your main password actually is, if you changed it)
- database host: localhost
- table prefix: wp_ is OK