The correct option is A start ... began
Both begin and start convey the same things, but there is a key difference in their usage. Begin is more formal than start, and is more often used for new activities being undertaken by people, whereas start is less formal and is used often to talk about inanimate objects / machines or to 'cause' something.. Thus, when talking about a book, we use start; and the activity undertaken is conjugated with the verb begin. Thus, Option A) is the correct answer. All the other options are inappropriate.