Book of Avalon Sidequest (Temporal Rift - The Hands of Time) | Final Fantasy XIII-2 Fragment Guide (#53)
Fragment Guide | Book of Avalon (#53)
Yachas Massif (110AF) - Temporal Rift: The Hands of Time Puzzle Guide
To unlock this quest you'll need to first complete all three of the red orb quests in Yaschas Massif (110AF), collecting Waltraute's Flower, Gerhilde's Blossom & Ortlinde's Bloom. Doing this will cause a time paradox to appear in the southwest corner of the map.
Go there, and investigate the paradox, bringing you to the Hands of Time Temporal Rift segment. The goal is to make every number on the clock disappear, though you can only eliminate numbers which have a clock hand pointing at it. Eliminating a number causes the clock hands to move from the now empty space to the left and right, in the number of spaces that the eliminated number specified.
There's many variations of this puzzle, but through brute force and luck you should be able to solve all four puzzles, getting Fragment of Time #53 - the Book of Avalon