categoryimage

<div>
<?php
    $taxonomy_name = 'product_categories';
    $termchildren = get_term_children( $term_id, $taxonomy_name );

    echo '<ul>';
    foreach ( $termchildren as $child ) {
        $term = get_term_by( 'id', $child, $taxonomy_name );
        echo '<li><a href="'.get_term_link($term->slug, $taxonomy_name).'">'.$term->name.'</a><img src="'.z_taxonomy_image_url($child->term_id).'" alt=""/></li>';
    }
    echo '</ul>';
?>
</div>

<?php if (function_exists('z_taxonomy_image_url')) echo z_taxonomy_image_url(); ?>