How to filter products by category in custom loop

Use $term->term_id instead of slug as the option value.

Check if the $_GET['product-category'] exists, then append it to the $args array.

 $args = array(
     'post_type' => 'product',
     'posts_per_page' => 6,
     'paged' => 1
 );  

 if ( isset($_GET['product-category']) && !empty($_GET['product-category']) ) {
     $args['tax_query'] = array(
         array(
             'taxonomy' => 'product_cat',
             'terms' => $_GET['product-category'],
         ),
     );
 }

 $loop = new WP_Query($args);