BuddyPress.org

Somewhat depends; are you only styling the highlighted li and li elements in comments as that has a bearing on the placement of the graphic.
Only the properties that actually change need be stated so you would really state your more generic li styles first, setting up the overall styling for a list in this parent or antecedent then state the more specific li elements with a class

So all li elements that have styles in common are declared first, something like:

ul.activity-list ul li {}

Then your commnets li styling

and lastly your more specific li.highlightpost-mine class which would carry only the styles needed to override existing ones or add new ones; If that is just a background color then as you have declared previously a ‘background’ stating color and image you would use background-color to override just the color otherwise you would lose the graphic.

If the background for those two elements is as wanted i.e you want the graphic on the activity-commnets li elements as well as the highlight class then it would be easiest to group the declaration and lose the background-position (shorthand statements cover all sub properties) so ‘position’ should be within the ‘background’ declaration

`
ul.activity-list li.highlightpost-mine,
div.activity-comments ul li {
background: #ebf7ff url(/images/ctr.png) no-repeat 100% 99%;
}
`