Display most popular posts of category

How about adding 'cat'=> 10 to your query?

$new_query = new WP_Query(  array(
   'posts_per_page' => $carousel_count, 
   'meta_key' => 'wpb_post_views_count', 
   'orderby' => 'meta_value_num', 
   'order' => 'DESC',
   'monthnum'=> $month,
   'year'=> $year, 
   'cat'=> 10
));