Image when sharng an article

Is that a blog layout of multiple articles, or is that one Joomla article?

In general, the answer is that Facebook uses the Open Graph tags set on the page to select the image. On the page you posted, there are no Open Graph tags set for images, so Facebook is 'guessing' at which to use. The solution(s) are to:
* Enable the Open Graph - Content plugin, if not already. This will automatically add og:image tags for the first image in the article so that it's used instead of having Facebook 'guess'.
* For more control, you can add the following tag into the content of the page:JFBConnect will replace that tag with the proper Open Graph tag. You can add as many of those tags as you want so that the share image picker will provide multiple options to the user.

After you've set that up, you can use the Social Debug tool to check your Open Graph tags and see what an example post would look like on multiple networks.

I hope that helps explain, but if not, let us know.

Thanks,
Alex

Glad to help, as always! Should you need anything else, just let us know.

Finally, if you haven't already, please consider leaving a rating and review for JFBConnect, or our support, on the Joomla Extension Directory. It certainly isn't required, but is very appreciated:
extensions.joomla.org/extensions/social-...ook-integration/7215

Thanks,
Alex