SQL query to search Custom taxonomy In wordpress

Question

I was trying develop a custom search box and I want to search custom post type taxonomy and I found this SQL query useful but there is one small problem, This query search all the available taxonomy on the database you can see my picture:

I search for green color from product category (woocommerce) but there is no such category created at my site this is coming from attribute taxonomy

SELECT DISTINCT wp_terms.term_id,wp_terms.name 
FROM wp_terms 
inner JOIN wp_term_taxonomy 
WHERE wp_term_taxonomy.taxonomy='product_cat' 
AND wp_terms.name like "green%";