Mark Zuckerberg wants analytics on daily Facebook users and messages from distributed data centers. He could write SQL queries to get this data from the distributed MySQL database. The document then provides an example query to find the daily users by counting user IDs grouped by last updated date. It also gives a sample query to find the daily messages sent by each user, grouping the message count by user and date. The document concludes with discussing collection frameworks in Java, concurrency, and having a Q&A session.