How should I connect the windings of this induction motor to make it work?
Your analysis certainly makes sense with respect to identifying the common point and the two pairs of windings. The resistance between M4 and M5 is indeed a mystery. I assume that you rechecked your measurements. There is a possibility that there is a short between the M4 and M5 winding at some point. If that is the case, it would likely be a fault rather than a feature of the motor design.

There are a lot of ways that single-phase induction motors are designed, but a 2/12 pole motor would need to have two completely independent sets of windings. Each set of windings would need to have the capacitor in series with one winding. It is possible that one capacitor could be used for that.

As mentioned in a comment, diagrams and other information is often attached to the back or inside the back of the machine. Any additional information that you can find would help. There are diagrams online for various designs of motors and washing machine control schemes. If you decide to apply power, it would be good to have an ammeter connected and know what current to expect. There should be a marking on the machine indicating maximum current.