Your MySQL databases can be fully managed from the MySQL Databases page. To delete a database just find Hosting → Manage → MySQL Databases:
In the section List of Current MySQL Databases And Users, click on ⋮ button in front of the desired database and choose Delete:
NOTES:
Deleting a database is a non-reversible action. Instead of deleting the database, you can clear it with just a few clicks.
If you want to save the copy of the database before deleting it, make sure to click on Backup first: