Agate has about the same hardness of quartz (6½-7 on the Mohs scale). I expect patience may have helped. If they did the carving with a slightly harder stone,

Agate has about the same hardness of quartz (6½-7 on the Mohs scale). I expect patience may have helped. If they did the carving with a slightly harder stone, it may have taken months to make (almost by keeping scratching it, rather than carving it), but it also would have been hard to mess up the work in a few seconds.