Ashish.. As a picture's worth a thousand words....The following pics are diagrams of the magnetic fields at ONE INSTANT in time when voltage is applied to the motor. The armature (rotating part) is considered as a magnet too (from the current induced in it like a transformer, hence "Induction motor". In the below diagrams only the main and start windings are shown, and this is VERY simplified, there are phase shifts due to the start capacitor, and more poles than are shown, normally, but the theory's the same. An instantaneous voltage is shown, and the resulting instantaneous magnetic fields. The magnetic poles of individual windings are shown as small N and S and the overall magnetic field as a large N and S.
Now reverse the polarity of the start winding and see what happens:
You see how the overall magnetic field has changed from one side of the main windings to the other. The result of this is that the armature will move one way or the other way when the motor is started.As pointed out in the quote of your above post, you need access to both wires of the start winding to do this. Sometimes the wires are internally tied together and you only have 3 wires coming out (common, main and start). If that's the case then sorry, your motor will only run one way....Does this make it clearer? Cheers // David