You must understand that there is more than one path to the top of the mountain.
-- Miyamoto Musashi

Let's find a good entry to start with

By good entry, I mean cubies that stick to each other in a correct manner, like the start status of the lower level scramble cases we saw before. But here we can't see any. Both W-O0 and W-O3 are yellow, but from the other stickers of the same cubie we can see that the two yellow stickers are just happened to be scramble together. They are not true neighbors. For the same reason, the X-O0 and X-O7 orange stickers are not true neighbors, either.

We can of course check W+ status, but it is not actually necessary at this stage.

Let's start with red

After staring at the puzzle for about one minutes, I think we can go with red. I mean X-O4 and X+O3. The former is red-pink(Y-O6)-green(Z-O1)-yellow(W-O5) and the later is red-pink(Y-O0)-green(Z+O3)-unknown(W+). These two have three common sticker colors, so they should be adjacent to each other.

My plan is to move X-O4 to W-O4 and X+O3 to W-O3. Interestingly, there are at least two ways to achieve this. First, let me show you the easier one. The idea is that, with a clockwise Y-twist to Z-, the X-O4 moves to W-O4. Since X+O3 is at the "top" of X+, it is not affected by Z- twists. X+O3 is in the other half of the puzzle. Similarly, we can apply a clockwise Y-axis-twist to Z+, so moves X+O3 to W-O3. Let's see the two twists:

The other way is more difficult. If you think about the relationship between X-O4 and X+O3, you can find that both are at the "Y-" side, which means that if the only cell you twist is Y-, the two will never be about meet each other. However, we can perform a "setup", twisting X-O4 to the Y+ side of the puzzle, then a counterclockwise Z-axis-twist to Y- will move X+O3 to W-O3. Then we can try to cancel the effect of the setup, and then perform a Z- twist to move X-O4 to W-O4. As the following clip:

Anyway, both can do the trick. You might ask, what are the differences? Are there any differences? Well, these unconstraint twists carelessly mess up other cubies, so actually they do differ. In fact, the differences matter for a speed cuber, because they often read the states very deep and analyze what approach is better so that they can "skip" more later steps. I am enjoying cubing in a different style in this series, so I didn't put attention on what were really changed other than the two cubies I care.

Now, we have done two cubies right? Sorry, I didn't see it until I put them together. Actually, the position is wrong.

How? I see adjacent red at W-O3/O4 and pink at Y-O3/O4, are they wrong?

Yes, they are wrong! At the observation stage, we knew that the two cubie share three colors (which also means that they form an edge that is shared by three different cells. 4D geometry!). But now, the green of W-O3 cubie is at Z+O4, while thegreen of W-O4 cubie is at Z-O3. The green stickers should belong to the same cell. Which means, we were wrong.

The good news is, we are wrong but not too wrong. We have aligned their two shared colors, only missing the rest one. Basically the red and the pink are correct. Then how to put the green stickers together? 3D physics intuition still works here. What we need is a Y-axis twist to W-O4 so that it goes to W-O2. The 180 degree twist should move the green sticker from Z- to Z+.

Another setup for W-O3 now. Exercise: which of the following really works?

1. Z-axis-twist the Z+ cell so that W-O3 goes to the Y+ half, then we do the mentioned 180 degree turn, and then cancel the setup by clockwise Z-axis-twist to Z+.
2. X-axis-twist the Z+ cell so that W-O3 goes to the X+ half, then we do the mentioned 180 degree turn, and then cancel the setup by clockwise Y-axis-twist to Z+.
3. neither.

Sigh. the answer is 3.

OK, I admit that 1 and 2 are my failed attempts. Actually 2 is quite close, but only lack of a second setup, because the first setup can not be directly canceled, otherwise the W-O2 will be move away. So the rough plan is

1. setup A, so that it won't be affected by step 2
2. move B to the correct position
3. setup B, so that it is not in the way cancelling step 1
4. resume A to the original position
5. resume B

It is tiresome to describe all these in words in a language I am not that good at. But to be honest, I have more and more feelings to the 2x2x2x2 puzzle as I write these. Anyway, as the following clip,

A more efficient way!

Learn to be aware which cubies are affected and what are not, you can see some moves that require only one setup, like

Requiring only 4 twists, cool!

Conclusion

Well, we have done two cubies, well done us! I believe it feels like weight training of the mind muscle using 4D dumpbells, and maybe you will wish gifs can be slow down a bit. Unfortunately, you have to practice yourself, that's the only way.

小結

初步了解如何正確拼接。