Method 1 – result-count.php
So if you copy
templates/loop/result-count.php from the WooCommerce plugin directory to your theme folder
woocommerce/loop/result-count.php, you can change just anything inside the new one.
It is not a preferable way, but I think you should know that is is also possible and all the code of that count is in this file.
Why not preferable? Because each time you update WooCommerce plugin, you have to check if there any changes in files you replaced.
Method 2 – Removing Action Hook
Once you insert the code below into your theme
functions.php file, the result count will be automatically hidden from all the archive pages like the shop page, product categories and tags and the search page as well.
remove_action( 'woocommerce_before_shop_loop', 'woocommerce_result_count', 20 );
One more thing – if you’re using StoreFront theme, you have to remove
woocommerce_after_shop_loop action as well.