How to get related category/categories in WordPress archive page

I usually do this by getting data from database 

$result = mysql_query("SELECT * FROM wp_terms JOIN wp_term_taxonomy
ON wp_term_taxonomy.term_id = wp_terms.term_id 
WHERE wp_term_taxonomy.parent = ".$parent_cat_ID." 
AND wp_term_taxonomy.taxonomy = 'product_cat'");

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