Query posts based on user preferences

Use get_posts with a taxonomy query:

$prefs = array(array('14','15'));
$args = array(
    'tax_query' => array(
        array(
            'taxonomy' => 'custom_tax_name',
            'terms' => $prefs[0],
            'operator' => 'IN'
        )
    )
);
$postslist = get_posts( $args );