How to set the background-position to an absolute distance, starting from right?
Use the previously mentioned rule along with a top and right margin:
background: url(images/img06.gif) no-repeat top right;
margin-top: 10px;
margin-right: 10px;
Background images only appear within padding, not margins. If adding the margin isn't an option you may have to resort to another div, although I'd recommend you only use that as a last resort to try and keep your markup as lean and sementic as possible.
In all modern browsers and IE down even to version 9 you can use a four-value syntax, specified in CSS3:
background-position: right 10px top 10px;
Source: MDN
There are a few ways you can do this.
Do the math yourself, if possible. You already know the dimensions of your image. If you know the dimensions of the div, you can just put the image at (div width - image width - 10, div height - image height - 10).
Use Javascript to do the heavy lifting for you. Pretty much the same method as above, except you don't need to know the dimensions of the div itself. Javascript can tell you.
A more hackish way would be to put a 10px transparent border around the top and right of your image, and set the position to
top right.