$wpdb->query( $wpdb->prepare(
    "INSERT INTO $wpdb->postmeta( post_id, meta_key, meta_value ) VALUES ( %d, %s, %s )",
    array(
      $this->_page_id,
      $metakey,
      $metavalue
    )
  ));

$this->_db->query( $this->_db->prepare(
    "INSERT INTO $this->_db->postmeta( post_id, meta_key, meta_value ) VALUES ( %d, %s, %s )",
    array(
      $this->_page_id,
      $metakey,
      $metavalue
    )
  ));

Catchable fatal error: Object of class wpdb could not be converted to string