Looking at the last two clues tells us that Amethyst is above Amber and that Amber is directly above Pearl. That means that Pearl is in the bottom row where there's only one position. Amber is also directly above Pearl (not diagonally above) placing Amber in the middle position in the middle row. We also know that Amethyst is in the top row, but we don't yet know which position.
Looking at the second clue tells us that Amethyst is far right of Agate. Assuming they are on the same row puts Amethyst in the top right corner and Agate in the top left corner.
With Agate, Amber, Amethyst and Pearl done only Jade and Lapis remains.
The third clue tells us that Lapis is far left of Jade. That puts Lapis in left middle row and Jade in right middle row.
This should be the correct solution unless I've missed something.
Looking at the second clue tells us that Amethyst is far right of Agate. Assuming they are on the same row puts Amethyst in the top right corner and Agate in the top left corner.
With Agate, Amber, Amethyst and Pearl done only Jade and Lapis remains.
The third clue tells us that Lapis is far left of Jade. That puts Lapis in left middle row and Jade in right middle row.
This should be the correct solution unless I've missed something.
Code:
Agate ---- Amethyst
Lapis Amber Jade
---- Pearl ----