It doesn't have to be photobucket, just as long as they're on the internet.
Right-click on the image and choose "Porperties" then you'll find the URL address.
When you're on the forum, there's a button while posting replies with a picture of a mountain on it, it's called "Insert image", Click this, enter the URL into the message you receive and the image should be there.
If the pictures are on Photobucket.com you'll find 4 textboxes under the image. Copy the box that says "IMG" into the forum.
I just tried clicking on your link, facebook requires login so I wouldn't recommend using it, as those of us without facebook can't see it.