Recently I had a client who wasn't happy with the images Facebook was providing as options when a user shared one of their product pages with Facebook.

You can give Facebook hints on what images you would like them to use.

Just add this code to your page for the images you would like to be in the selection:

<link rel="image_src" type="image/jpeg" href="http://example.com/images/my-image.jpg"/>

In my case, the image I defined here was the first choice that appeared on Facebook.

You can define more than one image for the available options.

Keep in mind when you are testing that Facebook caches the images for the link you are providing, so, if you make changes, they may not show up immediately unless you use a fresh URL to share.