Ah, I think I see the problem. The brown wires appear to be ground, so with the black meter lead on either brown wire the red wire on the white cable should read +12V which it seems to, and with the red probe connected to the red wire (which I would suggest moving to a blue or some other color wire to indicate -12V to avoid confusion) and the black probe still on the brown wire you should measure -12v/ If you put the black probe on the red wire on the black adapter cable (-12v) and the red probe on the red wire of the white cable you should get the expected +24V (and reversing the probes would then show -24 V as seen by the meter). I think you are hooked up correctly and just having problems with measurement. The meter sees the black probe as ground and measures positive or negative voltage relative to the red probe. Voltage is additive so if you put the black probe on -12V then the brown wire (ground) will measure as +12V (because it is 12V higher than -12V) and +12V will measure as 24V. You are likely correct that the two grounds on the white and black adapter cable are connected together internally in the adapter.
Peter
