But the sentences continue to elude me

Have you ever seen one of those images of a tesseract where it’s like a cube in a cube? (You can just look up “tesseract” to find an image)

Now, pick one of the corners of the outer cube and find the line that connects it to a corner of the inner cube. That’s our origin “edge” and we’re basically just going to move in through the cube along that direction.

There are three “faces” which share that “edge” (line). We do those ones first.

Then we move deeper in and do the three faces of the inner cube which share the corner our origin line connects to.

Then we have to zig zag around the six “faces” that exist between inner and outer cubes which are roughly perpendicular to our origin edge. (Imagine you broke the tesseract in half by cutting halfway between your starting corner and the corner opposite it. The “faces” we need to traverse would intersect that plane)

After that, we do the three faces on the far side of the smaller cube. (The ones opposite our starting corner)

Then we do the three around the line which connects that far corner of the inner cube to the outer cube.

Then we do the three faces on the outside of the large cube at that corner.

Finally we do the three faces on the outside of the cube around our starting corner.