could you do me a favor and take these books to my home?___

with pleasure： 1．愉快地、高兴地.如： I did the work with pleasure. 这份工作我做得很高兴.2． 十分愿意、可以（答应对方时的用语）.如：—Will you lend me the book?把书借给我好吗?—With pleasure. 可以.3．由于高兴,高兴得……. 如： Her eyes shone with pleasure. 她高兴得眼睛闪闪发光.
My / Our / A pleasure. 或 It is my / our / a pleasure. 不用客气（用来回答Thank you. 的答语）.如： —Thanks for helping me. —It is my / a pleasure.
综上所述,with pleasure 是对方提出要求,答应对方时的用语；my pleasure 是对方致谢时的答语.

my pleasure一般指对方答谢时的答语
而 with pleasure是指对方提出要求，你乐意接受