When you reach the Kara Kara Bazar in the Gerudo desert you will find these two men standing next to an unusual metal sphere and will give you the quest Lost in the Dunes when you speak to them. They have lost their friend in the storm and while it is their motto to stand in a conspicuous location to help them be found, the sinkholes in the area are going to make this difficult. They are correct, as he has been sucked into a sinkhole and you won’t find him roaming around the desert. Here is where to find him.
The sinkhole you need to find is very close to the Kara Kara Bazar. If you take the west road like the quest suggests, you will see a small fire next to a large rock to the left very soon after leaving the Bazar. If you look a little further beyond this, you will see the large sinkhole that the guys from the quest were talking about.
You will need to jump down into this sinkhole and immediately after landing in the cave below, you will find the guy that they were talking about. He is trapped in the cave and has no way to get out. If you search around the cave, you will find that several tunnels are blocked with boulders. You will need to use bomb arrows or fuse a rock to any weapon to create some kind of boulder-smashing weapon.
Once you have smashed your way through all of the tunnels in the cave and have found the exit, which is actually the bottom of the water well under the Bazar, the guy who went missing will come running out and make his way back to his friends. Return to them to complete the quest and he will also give you the metal sphere that you should bring to the Gerudo town to complete the Mysterious Eighth quest.