First you need "eyes of the godess" fragment skill, this will allow you to pan the camera around during events. While on a timed moogle puzzle do not start the puzzle but rather stand on the bottom number. You will have the ability to pan the camera up to see the top number. This will give you all the time you need to study a timed moogle clock puzzle without having the timer count down. When your sure you've got it figured out simply start the timer by moving into the clock area.