如果be busy 后面是名词则 是be busy with ； 如果后面是动词则是 be busy doing sth.
在你的句子中如果“准备”这个词用名词可以是前者,如果“准备”这个词用动词可以用后者.用with的话 是不是my brother is busy with his trip那用 doing 呢my brother is busy preparing for his trip.