In all things, one cannot win with defense alone. To win, you must attack.
-- L

Previously:

Where are we now?

We finished a face, the red-pink face. Theoretically we can say that we are already 25% finish the puzzle, because the 4 out of the 16 cubies are settled. We can then move on to finish either the red or the pink cell. Where are those cubies?

There are 3 red stickers not in W-. The Z+O2 is green-turquoise-red-???; the Z+O3 is yellow-orange-red-???; the Y-O5 is blue-red-orange-???. Coincidently, they are all belong to the W+ side of the puzzle, so we cannot see their 4th stickers, but that's OK. By deduction, we can tell Z+O3/Y-O5 should go to W-O6/W-O7 respectively.

As for lonely pink stickers, there are also three. The first two can complete the Z+ face of Y-. Z-O1 is green-blue-pink-gray, and Y+O4 is green-pink-gray-yellow. The former should go to Y-O3, and the later should go to Y-O2. The rest is gray-orange-pink-???. The 4th color is critical to decide it should go Y-O4 or Y-O5, but let's ignore it for now.

Let's go pink

Taking a break from red, let's go with the pink cubies.

The plan for Z-O1 is , moving the finished red-cluser out of W-, so that we can have a larger working space. So let's apply 180 degree of Z-axis-twist to Y-,

Then, applying a clockwise X-axis-twist to W-, the move will move the cubie's pink sticker to Y-, but it other stickers are in wrong positions. Green will be still at X- while it should be at Z+, blue goes to Z- while it should be at X-, but the fact that the gray sticker keeps itself at W- is a good thing. This means that we can perform one more clockwise Y-axis-twist to W-, to settle the green and the blue altogether.

Yeah, it looks good!

Is that easy or hard?

It takes only 4 twists to settle the 5th pink cubie, but actually I stare at the screen for about 1 hour now. It's funny. Those who have any experience on twisty puzzles must agree with the following statement: the puzzle is not yet stated because all the positions are settled with intuition. Later on, we will definitely need to use some algorithms. We don't have any, so we have to develop some.

By the way, the term algorithm in the cubing community has nothing to do with coding. It means a certain sequence of twists that can fearlessly breaks established cluster, move some cubies to the place you want it to, and then amazingly restore the mess at the end. The reader can check J perm's video for more explanation.

Actually at the stage, in which 5 cubies are done in a cell (now it is Y-), the only "free" cell is its opposite cell, Y+. Y+ is free to do any twist, at the same time the Y- cell is no affected at all. For all others, it is not the case. This is a property of any hypercube puzzle: As you half-done a n-cell (n = 3 now because the total puzzle is in 4D) with one more cubie, it is inevitable that only the opposite n-cell can remain free. It will be easier to imagine if we center either the cell or its opposite cell, but I will leave it to the reader as a mind experiment.

Knowing the fact won't directly help us solve it, but it gives us enough bravery. There is impossible to complete the 6th, 7th and 8th without breaking the finish status temporarily. So basically, the low hanging-fruits has been picked, things will be harder from now.

Anyway, let's move on

The pink cubie of interest is now at X-O4, it should go to Y-O0. Yes, the plan will be complicated, so I want to break it into two halves now. The first half, I have no idea what to do precisely for now, but we must break the 5-pink-cubie cluster to make room for us to twsit X-O4 into a good position. The second half must be something like the following: the 5 cubies stick together as if the cluster is never touched (but actually it was in the execution of the first half). One more condition is that, the 6th cubie is waiting to join its fellow cubies, with a correct/convenient orientation settled, at X-O0. With the two conditions, we apply a clockwise Z-axis-twist to X+ which shift Y-O3/O4 to W-O3/O4, then a Z-axis-twist to Y+ can shift X-O0 to join the 2-pink cluster, and then a counterclockwise Z-axis-twist to X+ agian to shift the 3-pink-cluster back to Y-, finishing the Z+ face.

Planning backwards helps us imagine the details in the first half. We have to make sure the X-O4 can go to X-O0 with a suitable orientation. The good news is, a simple 180 degree X-axis-twist to X- can move X-O4 to X-O0 with the orientation we want (yellow at the pink's X+ side, gray at the Y+ side, and green at the Z+ side), but tis bold move definitely breaks Y-.

After staring for about one more hour and some trial-and-error, I found a sequence to achieve the first half plan. It is a long sequence, so I will break it down to a few clips.

Now the cubie has go to the X+ side of the puzzle with its pink at W-O4. The 2-pink cluster in Y- is at the X- side of the puzzle, so we don't have to worry about them now with regards to twist W-O4. However, the 3-pink cluster in Y+ has one cubie in the X+ side, so W-O4 is not totally free to twist. Furtunately, the 3-pink cluster in Y+ is kind of free, so they can escape to X- side of the puzzle. The, with the 5 done cubies at the X- side, W-O4 can be 180 degree twisted to W-O0. The described sequence is as follows.

Now we are in the closing of the first-half. We have to resume the 5-pink cluster. Interestingly, the Y-axis-twist to Y+ move W-O0, the cubie we just setup, away from a good position, but after we move the 3-pink cluster back to Y-, the now-at-W-O7 pink sticker is at the Y+ side of the puzzle, so it can resume its position to W-O0 again freely, as follows,

Then we can go for the second half of the plan. Oops, we also forgot to resume the 2-pink cluster in Z- part of Y-.

Yeah! What a sequence...

Conclusion

We now successfully finish 2 more cubies, forming a second face. The steeply increasing difficulty is a little bit scary. To be honest I didn't expect to take so much time to just finish 6, 3/4 of a cell. Anyway, the show must go on.

小結

完成了 2x2x2x2 的第二個面。順帶一題，沿用既有翻譯的話，cell 為胞。