Add category_name or cat
in your arguments
(args) array.
<div id="mini_stream">
<ul>
<? $args = array(
'post_type' => 'post',
'posts_per_page' => 4,
'category_name'=>'html',
);
$loop = new wp_Query($args);
while($loop->have_posts()) : $loop->the_post();
echo '<a href="'.get_permalink().'">';
echo get_the_post_thumbnail($post->ID, 'category-thumb');
the_title( '<h6>', '</h6>' );
echo '</a>';
endwhile;
wp_reset_query(); ?>
</ul>
</div>