He is preparing for his doctoral qualifying examination.

doctoral 是由名词 doctorate（博士学位）去掉词尾 -ate 加上形容词后缀 -al 构成的形容词，表示"博士的"或"博士学位的"。qualifying 是动词 qualify 的现在分词形式，qualify 意思是"使具有资格"，qualifying examination 指"资格考试"。