Something about that doesn't look right. If you measure between the black and red leads on the connector to the white cable from the adapter do you see +12V? If not, I'd check the wiring on the adapter board as pin 1 should be connecting to the pin on the end of the connector (which in turn should be the center pin of the plug from the adapter) and pin 2 should be going to the barrel of the plug. From what the voltmeter is reading I suspect you will find the black and red wires on the right hand (white wire) barrel connector are backwards, i.e. red is ground (and thus the -12v to the red wire on the other connector which looks to be connected correctly). If that is true then if you move the red meter probe to the black wire on the same connector you should see the expected 24 volts.
Peter
