Retrieve the list of categories for a post with custom query

Hello everyone, I want to display on index the category name of posts with an custom query like this:

<?$pop = $wpdb->get_results(“SELECT id, post_title, comment_count FROM {$wpdb->prefix}posts WHERE post_type=’post’ ORDER BY comment_count DESC LIMIT 6”);

foreach($pop as $post) : ?>
Category: <?php
$category = get_the_category();
$cat = $category[‘$id’];
foreach ( $cat as $key => $value )
echo $value;?>

Any idea?