How does the commutator work right here?
The individual physical coils of the armature are connected in series around the ring. When you make contact with two of the segments of the commutator, you are essentially forming two parallel "virtual" coils that are composed of the individual physical coil segments on either of the two paths between the contacts. These virtual coils have the desired alignment with the stator field in order to achieve the desired result. Each physical coil segment experiences an EMF that is related to its actual physical angle with respect to the stator field, which explains the numbers in your Figure 4.11b.

As the armature turns, the virtual coil turns with it, until you get to the point at which a different set of commutator contacts is reached by the brushes. At this, point, you get a different combination of physical coils, and the resulting virtual coils have an alignment that is reset back to the beginning of the desired alignment angle.

In this way, the armature experiences the maximum amount of torque available at all times. More physical coils and commutator segments means that the torque ripple is reduced and the efficiency is increased, at least to a point.