A friend put up some photos and I hate the one she put up of me. Can I keep it from
Appearing on MY Facebook site?

I think this is how you do it:

First go to Settings, then go to Privacy Settings, then go to Profile.

Go down to Photos Tagged of You and hit the arrow next to the box. Then hit Customize. Then click on Only Me, and in the Networks box make sure it says None of My Networks.

After you do all this it should work out that you're the only one who can see those photos from your site. They'll still show up on your friend's page, though. There's nothing you can do about that.

You can, of course, tell your friend to take it down. If he/she won't do that, not much of a friend.

You can just untag yourself from the pic

If she put the photo on her page about your, I do not believe you can do anything since you can't remove a photo from her web page.

You can ask her to, and if she will not, try contacting Facebook