Decide which of the final rewards you wish to obtain (see chart below).
Trade Yurim the proper "base" item and colored chip.
IMPORTANT: Once the "base" Item and colored chip are traded, you are committed to that item and can not get another until that is complete. For this reason, it is recommended that you not trade the first items until you have all of the organs in hand as well.
Talk further with Yurim, for information on her research.
Trade an Apple Pie to Yurim (optional), for more hints on how to finish the research steps.
Go to Al'Taieu and obtain the necessary items as shown in the chart below.
Return to the Tavnazian Safehold and trade all the organs (all at once) to Yurim to receive your reward and complete the quest.
Other chips will work as a base item for the earrings. It is confirmed that trading a purple chip or a green chip will produce a Sanative Earring, and trading a blue chip or a yellow chip will produce a Relaxing Earring. It seems likely that the Light element colors (White/Purple/Red/Green) will produce a Sanative Earring and Dark element colors (Black/Yellow/Blue/Clear) will produce a Relaxing Earring, but only Black, White, Purple, Green, Yellow, and Blue have been confirmed.
To see which gorget would work best for you, go the item's page to see which weapon skills it works for, or look at this chart.
The Hachirin-no-Obi can be crafted from all 8 obis, Synergy Craftsman level. The Fotia Gorget can be crafted from all 8 gorgets, Synergy Craftsman level. There's also a set of level 87 elemental belts that drop from Abyssea NMs and can be crafted into the Fotia Belt from all 8 belts, Synergy Craftsman level.
Completing any item in this quest allows you to begin trade with Meret.
Yurim (Second Floor, Tavnazian Safehold)
Yurim wants to show you the fruits of her research, but lacks the materials to begin the final stage of the experiment. You know what you have to do!