Running two inputs 180° out-of-phase puts the peaks and valleys of the sine wave so that they null each other out when summed (see the middle picture below). This has a tendency to cancel out both inputs, and is quite pronounced in the "far" field, but negligible in the "near" field. Normally phase cancellation is undesirable, but when you know what you want (and in this case, what you don't want) then you do it deliberately.
I found an illustrated example here
- click to see the full animation and explanation.
Yes, you can start with an adapter like the one in the picture
Open one of the female connectors, unsolder, reverse and resolder the wires running to pins 2 and 3.
It looks like you might want an adapter with longer cables. Those look very short.
Pete (user Drumr) wrote to me a couple of weeks ago, about how he made the cable.
" Okay...I made the cable tonight. Pretty simple;
Cut the male ends off the two "to mic" cables,
and the female end off the "to mixer" cable.
Took the exposed wires on the "mic" cables and soldered the ground to ground and swapped the black & white (pin 2&3) wires and soldered.
Then took mixer end cable and soldered ground to ground and the two other leads to the other two...no way to screw it up. Heat shrink tubed the whole works...very nice looking job.
Tested it with a couple mics and they both work.
No way to test the phase really, but they both sounded fine to me.
edit - correction about low frequencies and added clarification about near and far fields...