This page explains how to find the Kah Yah shrine and solve the "Quick Thinking" puzzle.
How to Reach the Shrine
You might want to activate Faron Tower before looking for this shrine.
Also, it's easier to find this shrine at night, so you might want to bring wood and flint, or a flame weapon to light the wood.
One way to go to this shrine is to go to Muwo Jeem Shrine and jump off of the south side of Cape Cales, then float down to the beach down below.
Another way is to go to Yah Rin shrine and go east through Lurelin Village and Gogobi Shores to reach Palmorae Beach.
You will see someone standing by the Palmorae Ruins on Palmorae Beach. Talk to him and ask what he is doing, then ask if you can help. He says that the fragments glow at night.
One of the shards is to the east, in an alcove in the cliff wall. Take a picture of it, then go back and talk to Garini to show it to him. He recommends looking in the water next.
One is to the south of the ruins, in some rocks next to some wooden barrels and crates.
After you show him the second fragment, Garini says that the currents might have carried the fragment to Cape Cresia or Soka Point.
Go southwest from the ruins, then go east along Cape Cresia. Go all the way to the end of Soka Point. The shard is at the base of the palm tree.
Talk to Garini and he will decipher the message if you have taken pictures of the three missing shards.
Then stand on one of the glowing orange platforms and kneel (push the left control stick like a button). Garini will do the same, and the shrine will appear.
How to Solve the Shrine
There are two moving platforms in this shrine. Each platform goes toward a switch near the far wall of the room. You have to put a barrel on the switch to hold open the bars.
On one side, you need to get on the moving platform with the barrel, then set it down. After you go through the first archway, shoot an arrow at the crystal switch to raise the bars in the second archway, then after going through the second archway, hit the crystal switch again to raise the bars in the third (and first) archway. Then put the barrel on the switch at the end. This opens the bars, so you can open the chest to get a Knight's Claymore.
On the other side, you need to get on the moving platform and put the barrel on the side of the platform so it won't get pushed off by the wall, then you need to crouch to avoid getting pushed off by the second wall, and then you need to move the barrel to the other side of the platform (or pick it up and stand to the side) so you and the barrel don't get pushed off by the final wall. Put the barrel on the switch at the end to open the bars. Open the chest beyond the bars to get a small key.
Use the small key to unlock the door between you and Kah Yah. Talk to Kah Yah to get the Spirit Orb.