We had one of our motion lights go out after 14 years. I changed the bulb, still will not work. We bought two matching lights, (led) lanterns from Home Depot. Hooked up white-to-white, black-to-black and bare copper of fixture to bare copper in junction box. One box has two whites twisted together and two blacks twisted together; there is also two bare copper wires twisted together. The other box has one white, one black and one bare copper. I installed the lights and the one on the left, (2 blk, 2 what, 2 copper) worked, the other ( 1 white, 1 black, 1 copper) did not. Called Home Depot and they said check for a broken wire in the first box, I did and found that one of the blacks was broken. I added a piece of # 12 romex to the broken wire and twisted together and placed a wire nut on the twisted black wires. Hooked up the lights, black-to-black, white-to-white, bare copper from fixture to bare copper in box. Installed the other light to the box with one white, one black and one bare copper. Turned on power and the light with 2 black, 2 white worked, the other light did not. Checked power in boxes. 2black/2white boxes had power on black wire only, the other box has power to both black and white and will not operate the light. This circuit is off a dual throw 20amp breaker and there is two additional wall sockets in the kitchen on this circuit. There is a wall switch in the foyer that operates the lights. Any help you can give will be greatly appreciated.

If, as you say, the lights are operated off a switch in the hallway, then you need to have a close look at the switch.

There are two ways to wire a switch into the circuit. If power is supplied through the switch, then you should find a black/white w/ground at the switch. Only the black wire will be connected to the switch. The switch interrupts the source in the OFF position. The source black connects to the bottom screw of the switch. The feed to the lights connects to the top of the switch.

The other way is via a "switch loop" This method will have the source (feed) at the light and a loop arrangement to the switch. What you would have is the Black feed is connected to the bottom of the switch with the white wire. A black band of tape or marker should be placed on the white wire going to the switch.

The black wire from the top of the switch is called the return. You would connect this wire to the black wires feed both of the lights. The whites from the lights and the white from the source would be connected together and of course the equipment grounding conductors would be connected together.

So, please look at the switch and let us know what switch arrangement you have.

Your description of the breaker makes no sense. A dual breaker (one on top of the other) is a typical 240 volt arrangement. If you are using wall receptacles than you would not be using 240 V (if you are here in the U.S.A.)

Are you talking about two "slim-line" breakers mounted in the same slot? Or possibly a shared neutral arrangement?

Can you take some pics and attached them to this thread so we can see what is installed?

Dual throw breaker, as Don notes is 240VAC. Are you sure you don't mean a mini breaker with 2 separate switches? The way you have described the wiring sounds right for a 2 light system, Power comes to the box with 2 blacks and whites and then goes to the 1 black and 1 white box. However, we have no idea as to how your wiring was installed. Look at the switch that controls the light and tell us what color wires are on the switch.

the other box has power to both black and white

Tell us what that means and how you determined that.