Which sentence is punctuated correctly? a. many of bush’s experiences are chronicled in her book barbara bush: a memoir. b. many of bush’s experiences: are chronicled in her book barbara bush a memoir. c. many of bush’s experiences are chronicled in her book: barbara bush a memoir. d. many of bush’s experiences, are chronicled in her book barbara bush a memoir.

The correct answer is A. Many of Bush’s experiences are chronicled in her book Barbara Bush: A Memoir. 
In the sentence above, you should place the colon within the title of the book itself - in order to separate the genre of the book (a memoir) from the title of the person who wrote it (Barbara Bush). Placing the colon anywhere else would be grammatically incorrect. You could also add quotation marks around the title, but that is not one of the options here.