what i have been busy with recently is---the college entranc

这里跟 busy with 没有关系.
先看看句子结构.
What I have been busy with recently is ? the college entrance exam.
这句子可以这样分开
(What I have been busy with recently) (is) (? the college entrance exam)
第一个 () 是 subject 主语.
第二个 () 是 verb 动词.
第三个 () 是 object 宾语.
就是说,英语句子基本结构已经出现了 (subject + verb + object).
首先,看主语 what I have been busy with recently.当中的 what 提示了宾语一定是名词.
这样想的话,A 和 D 已经不对,因为他们都不能配合 ? the college entrance exam 成为一个名词.
那究竟是 B 或是 C 呢?那就得看 prepare 后的 preposition 是什么.我们说 prepare for something.意思是为某事准备.所以,C 是错误的,因为 preparing myself TO 那个 to 不对了.
剩下的 B 自然就是答案.