How do you break down these puzzles?
Try to look at the rules you're given collectively to work out placements that must go a certain way, and then once you have one or two you can work out everything in relation to those. For example, in the first shrine puzzle one of the rules is 'Agate: Lapis is west of me' and there are only two spots that can
have anything west of it so you already know those two gems must occupy either the top or bottom two slots. Then you look at the rule for Lapis and you see that it says that Pearl is to the southeast, which means you know Agate and Lapis must be the
top two spots on the puzzle because that's the only way for both rules to be true. At that point it's easy to work out the rest.
For another example from the last puzzle in the same location, two rules taken together let you nail down Lapis' location because one says that Agate is to its northeast (so it must be the middle or bottom spot on the left column) and another says that Lapis is north of Pearl (so it can't be the bottom spot and
must be in the middle row). Getting that also lets you place the two other gems because there aren't any other places those can fit under the rules provided.
There are a couple of things to watch out for. As already mentioned there can be multiple valid spots if you look at a single rule in isolation so don't assume it's necessarily the one closest to the gem that's the subject of the clue. Also there's one puzzle that has tripped multiple people up so remember that 'adjacent' includes diagonals.
