Ivan summed it up nicely. There's no way to sync likes so that a Like button for your Home page has the same Like count as that for your Facebook Page. However, you can include a Like button on your home page that, when Liked, will Like your Facebook Page.
To do so, if using the JFBCLike module, simply set the URL to your Facebook Page URL. If using the JFBCLike tag, use the following syntax:
{JFBCLike href=https://www.facebook.com/your-page-url}
Hope that helps,
Alex
How to integrate my web page with my facebook fan page
