(WARNING: MAY BE A SPOILER)
This puzzle is quite probably the trickiest one in the game. If you pay a lot of attention, however, it is possible to achieve. After Pandora's Box is opened and you have acquired the mirror, you will then need to go melt the ice in the upper right room of the sketchbook with said mirror. After melting the ice with the mirror found in the box, there will be a start to finish line in the room that you enter. There is also an arrangement of eight buttons on the floor of the room as well. The start to finish puzzle line starts with (and goes in order) with a heart, an eye, a crescent, a sun, a star, a spiral, a cherry, and a pair of lips (it looks like a smile face in the line puzzle). If you leave that room to go outside, go have a look around the entire sketchbook (but be careful, as there are random objects that can be thrown at you from literally out of nowhere). You will notice a heart on the door of the house in the upper middle room that was not there before you opened Pandora's Box. If you have a even bigger look around, you will find that there are other icons that were not around before you opened the box. In the room with the house and the butterflies (mid-left room), you will notice that there is a new butterfly flying around that when observed, it will say that it has an eye-like pattern on its wings. In the upper-right room with the pond, you've got to "stare into the water" to make the crescent shape appear on the surface. In the upper-right room you will notice that that sun is there (that was not there before Pandora's Box) and that it is part of the puzzle. In the room with the house that has a creepy crayon man drawing in it (one of the first rooms you encounter in the Sketchbook), if you observe one of the bookshelves you will notice that there is a star icon on one of the books. After leaving that house and going to the part of the sketchbook to the immediate left, you will notice a spiral that is on the billboard. Next if you go to the tree room, you will notice that all the trees have gotten leaves and fruits on them. But on one of the trees to the left, you will notice that there is a cherry that is out of place. Take note of that. Now onto the bottom left of the sketchbook (for investigative purposes), there is a pair of lips and teeth to the far left of that room. Now with all this new information about the changes of Pandora's Box, you should be able to come up with a table. If you piece together the rooms (there are nine rooms, and eight buttons in the puzzle room) you should possibly get a table like this.
Now while in the puzzle room, take that start to finish puzzle and arrange the icons to the rooms where you saw them, and put numbers in order of start to finish. You should get a table like this now.
Now simply press the buttons in order starting with 1st and ending with 8th. Once you have pressed all the buttons in that order, the Plastic Key will appear in the center of the room.