rewriting for custom taxonomy rewrite

All you need is pass the URL structure in the arguments when registering your custom taxonomy. For example:

add_action( 'init', 'register_my_taxonomy' );
function register_my_taxonomy() {
    $args = array(
          //Complete the arguments for your taxonomy
          // The rewrite argument should looks like this
          'rewrite' = array( "slug" => "cars/my-tax" )
     );
    register_taxonomy( 'my-tax', 'my-post-type', $args );
}

You may need to flush the rewrite rules; you can do it just visiting the permlink settings page in you wordpress admin area.

Also, if you have a custom post-type called ‘cars’, it is possible that you get a PHP error when viewing the tax archive pages in the front end using the URL ‘cars/my-tax’. You can suppress this error with this:

/*
This supress an error with Undefined property: stdClass::$labels in general_template.php
See: http://wordpress.stackexchange.com/questions/71157/undefined-property-stdclasslabels-in-general-template-php-post-type-archive
*/
add_action( 'parse_query', 'wpse_71157_parse_query' );
function wpse_71157_parse_query( $wp_query ) {
    if ( $wp_query->is_post_type_archive && $wp_query->is_tax ) {
         $wp_query->is_post_type_archive = false;
    }
 }