Begin by logging into Horde.

Click the "Mail" icon at the top of the screen.

horde-mail-icon

Next, click on the "Folders" icon at the top of screen.

horde-folders-icon

Select the box next to "Inbox" and from the Choose Action drop down, select "Empty."

horde-select-inbox

You will receive a notification that you are deleting all messages in the Inbox. To confirm, click the Empty Selected Folders button.

horde-confirm-empty-inbox

The process can take several minutes, and depends on how many messages are in the Inbox.