…to show the subcategories of a specific category (ID 89) …
Try this
$product_cats = wp_get_post_terms( $post->ID, 'product_cat' );
if ( ! empty( $product_cats ) && ! is_wp_error( $product_cats ) ) { ?>
<ul>
<?php
foreach ($product_cats as $childcat) : ?>
<?php if ($childcat->parent == 89)) { ?>
<li>
<a href="https://wordpress.stackexchange.com/questions/331894/<?php echo get_term_link($childcat->term_id); ?>"><?php echo $childcat->name; ?></a>
</li>
<?php } ?>
<?php endforeach; ?>
</ul>
<?php } ?>
I hope this helps.