Show how many images are attached to a post/page on compose page

add_action( 'add_meta_boxes', 'attached_images_meta' );

function attached_images_meta() {
    $screens = array( 'post', 'page' ); //add more in here as you see fit
    foreach ($screens as $screen) {
        add_meta_box(
            'attached_images_meta_box', //this is the id of the box
            'Attached Images', //this is the title
            'attached_images_meta_box', //the callback
            $screen, //the post type
            'side' //the placement
        );
    }
}
function attached_images_meta_box($post){
    $args = array('post_type'=>'attachment','post_parent'=>$post->ID);
    $count = count(get_children($args));
    echo '<a href="#" class="button insert-media add_media" data-editor="content">'.$count.' Images</a>';
}

The above will link to the media uploader. I added the link because the screenshot you posted looked like a link. Feel free to remove the link like so:

echo $count.' Images';

Just pop this in your functions.php, custom plugin, etc.