Because you are on a page and not in the template that showss the posts you need to supply a post ID from a post that the field is attached to.
This means that the first thing you’re going to need to do is to get a post and set a valued for $post_id, then add that argument to the get_field_object call.
<?php echo implode(', ', get_field_object('example', $post_id)[choices]); ?>
