It appears that you forgot to close your PHP code correctly using ?>, try the following:
<li class="fb-like fb" data-href="https://wordpress.stackexchange.com/questions/110669/<?php the_permalink(); ?>" data-layout="button_count" data-show-faces="true" data-send="false"></li>
For the future, you can easily view the source of the page and check if the_permalink was correctly inserted.