limit number of tags shown in tag.php

If you want to modify the main post query, use the pre_get_posts filter:

add_action( 'pre_get_posts', 'limit_tags_to_196_posts' );
function limit_tags_to_196_posts( \WP_Query $query ) {
    // we only want tag archives
    if ( is_admin() || ! $query->is_main_query() || ! $query->is_tag() ) {
        return;
    }
    $query->set( 'posts_per_page', 196 );
}

Notice that we check the query first, we don’t want to change all queries everywhere or we’ll be changing WP Admin or RSS feeds, etc, we only want tag archives