To find the next time the two alarm clocks will ring together, we need to find the smallest common multiple of 9 and 12. The least common multiple of 9 and 12 is 36, which means that after 36 minutes, both alarm clocks will have completed their respective cycles and will ring together again.
Starting from 2 p.m., 36 minutes later will be 2:36 p.m. Therefore, the two alarm clocks will ring together again at 2:36 p.m.