The format for using TwitterOAuth is get('path', ['param' => 'value']); So what you’ll want is this:
$this->connection->get("direct_messages/show", ["id" => 852275615017426947]);
Your snippet would create a URL like this which is not valid:
https://api.twitter.com/1.1/direct_messages/events/show?id=852275615017426947.json