first read more is due to just <?php
$query = new WP_Query(array('cat'=> '4', 'posts_per_page'=> '6', 'orderby'=>'modified', 'order'=>'DESC'));
while ($query->have_posts()) : $query->the_post();?>
<strong><?php the_title();?></strong>
<?php if ( get_post_meta($post->ID, 'read_pdf', true) ) : ?>
//replace read more link to value of read_pdf key if exists
<a href="<?php echo get_post_meta($post->ID, 'pdf_key', true) ); ?>">
read more
</a>
<?php else : ?>
//show normal read more link if no pdf attached.