I'll give it a whirl. I assume you're talking about you PM inbox.
Go to your PM's.....look in the top right corner and or to the side of the window. You'll see a little box. See picture below.
Now, click the box in the top right corner (red circle) and it'll automatically select 'ALL' your messages. See picture below.
Or, if you want to delete some and keep others, you can simply check the boxes individually. See picture below.
Once you've selected the messages you want to delete, scroll to the bottom and you'll see some additional choices. By default you'll see the message 'move to folder' in the window. AND since you want to delete these messages, you'll need to click the little 'down arrow' (red circle) to display a 'drop down' box of additional choices. Select 'Delete'.
You'll also notice the 'Go' button to the right indicates that I've got (5) messages selected.