Finding the missing pages of the Botanical Atlas on your Farm is not too complicated. When a new Botanical Plate appears around your Farm (every 20 hours), click the Hint button (magnifying glass) at the left of the task in question and an arrow will point to it.
The only “hard” one is the 4th Plate that can be found inside the Train Tunnel.

Botanical Plates on the Western Lands
After you send Joe to study all 9 of the first Botanical Plates, a new Quest will appear, aptly named “Botanical Atlas Reconstruction 2”. In it, you will have to find 5 more Botanical Plates on the western lands to the Farm.
The Factories (3 Botanical Plates)
We’ll start with the hardest Botanical Plate to get, the one that appears to be on a ledge.
Joe can reach the Plate from your Farm, from Alpaca Hill (above the train tracks, go left with Joe). When you reach the ledge in The Factories, get Joe to grab the plate, then return the same way back to your Farm.

The next one is in the Southwestern part of The Factories, below the road bridge.

And the last one is the Northern Part of the Factories, in the Breezy Tulips Area.

Water Sawmill (2 Botanical Plates)
Joe can reach the Water Sawmill North or the Water Sawmill South area depending on how he gets there from The Factories.

The Plate in the Water Sawmill North is above the road, right at the top, and the one in the South is next to the fenced area.

