Okay, it has been decades since I looked at windings for consequent pole machines, so my answer could be _very_ wrong.
You have 12 'pole phase groups', and I was confused because you called each group a 'coil'. I would say each group has 4 coils, but as long as we understand it is fine to call a 'pole phase group' a coil.
Groups 1, 4, 7, and 10 are all part of the U phase. 2,5,8, and 11 are V, and 3,6,9, and 12 are W.
In one mode you supply power to U1, V1, and W1, and short U2, V2, and W2 together. U2, V2, and W2 form a star point parallel to the permanent star point in the motor. In this mode groups 1 and 7 have the opposite polarity from 4 and 10, and 1, 7, 4 and 10 are all see the full L-N voltage. At a given moment in time, when group 1 is N, group 4 is S, group 7 is N and group 10 is S. In this mode you would operate as a 4 pole machine.
In the other mode you leave U1, V1, and W1 open, and supply power to U2, V2, and W2. Trace the current flow from U2; you go through group 4 and 10, then to the U1 node (not connected to anything) then through groups 1 and 7. On this path, the 'sense' of current flow through all the coils is the same, at a given moment in time, when group 1 is N, group 4 is N, group 7 is N and group 10 is N. In this mode each coil sees half of the L-N voltage, and the machine operates as an 8 pole machine. This is called 'consequent pole' operation; when group 1 and group 4 are both N, there must be an S pole in the gap between them.
Hope this helps. Like I said I've not worked with this for decades, so take the above with a grain of salt and see if it helps you get a self consistent understanding.
Jonathan