AddThis button + Facebook Like button


I am trying to use AddThis button on a web page of mine, which you can share, like (facebook), and tweet (twitter) -

the AddThis code is pretty straight forward below,

<!-- AddThis Button BEGIN -->
    <div id="share" class="addthis_toolbox addthis_default_style ">
    <a class="addthis_button_facebook_like" fb:like:layout="button_count"></a>
    <a class="addthis_button_tweet"></a>
    <a class="addthis_counter addthis_pill_style"></a><!---->
    <script type="text/javascript" src=""></script>
    <!-- AddThis Button END -->

but I don’t understand - in the code above, where can I put the image or video url which I have uploaded and posted on my fb page? for instance the url below is the image from my facebook page that I want to track how many people like this picture through my website,

I have read through the documentation on AddThis but it doesnt explain this at all!

It points me to this,

again, this is a facebook API but not AddThis API. If I am using the Like button from the facebook API, then I cannot AddThis API above, can I?

furthermore, The Like button from faebook API seems to work on the facebook page, but not the individual picutre or video I uploaded/ posted on my facebook page, for instance, I tried this on my localhost, the picture on my facebook page won’t collect the number of like even though I have clicked the Like button on my screen.

<script src=""></script><fb:like href=";set=a.10150115644754972.329183.55239684971" layout="button_count" font="arial"></fb:like>

so my main doubt on the Like button itself - does it work on facebook only or does it apply to the individual picture/ video on my facebook page? I tried to find this answer from the [facebook Like documentation][2] but it doesn’t explain anything about this.

it would be grateful if you have any idea. thanks!