Join both white cable wires and solder them together.

Remember that the white wire from the AC adapter NEEDS to be soldered to the white wire from the cable that comes from the MacBook connector.

The black insulated cover tube on the cable is to isolate the cable later, you can use heat to shrink it.

The last pic shows the black insulated cover tube, you can cut it up to fit the length you need.

It is very important to isolate both wires, they cannot touch each other or else they will short circuit (in other words: Kaboom!).