wp-filter-by-tax.php

function filter_projects_by_taxonomies( $post_type, $which ) {

    if ( 'project' !== $post_type ) //your post type name instead of 'project'
        return;

    $taxonomies = array( 'type' ); //your post type taxonomy name instead of 'type'
    foreach ( $taxonomies as $taxonomy_slug ) {
        $taxonomy_obj = get_taxonomy( $taxonomy_slug );
        $taxonomy_name = $taxonomy_obj->labels->name;
        $terms = get_terms( $taxonomy_slug );
        echo "<select name='{$taxonomy_slug}' id='{$taxonomy_slug}' class='postform'>";
        echo '<option value="">' . sprintf( esc_html__( 'Все %s', 'text_domain' ), $taxonomy_name ) . '</option>';
        foreach ( $terms as $term ) {
            printf(
                '<option value="%1$s" %2$s>%3$s (%4$s)</option>',
                $term->slug,
                ( ( isset( $_GET[$taxonomy_slug] ) && ( $_GET[$taxonomy_slug] == $term->slug ) ) ? ' selected="selected"' : '' ),
                $term->name,
                $term->count
            );
        }
        echo '</select>';
    }

}
add_action( 'restrict_manage_posts', 'filter_projects_by_taxonomies' , 10, 2);