The wire in question is that top wire. The black one with the red stripe.
Best Answer
It looks like feeder wire, probably stranded aluminum—though it could be copper. Judging by the scale of the breakers it looks to be AWG 6 or 4. See this chart for ampacity ratings.
If you inspect the jacket of the wire for up to 18 inches, you should be able to find some writing which gives the exact wire size (gauge number), temperature rating, and voltage rating of the insulator. Also, many cables have a distance number, usually in feet, from some origin (maybe the beginning of the 1000' spool the wire came from).
What you have is a switch leg. In the past it was a best practice to wire the white hot so it was not confused as a neutral the white was supposed to be marked with a different color than white or green with tape or paint marker, but that step was not always done in the past by pro's and rarely by DIY folks, I usually carried a black marker and marked them but not always to tell the truth. With white being hot the power is being fed from the fixture on the white to the switch and then with the switch in the on position you will find it is also hot allowing the power to flow to the fixture.
The two hots must have 240V voltage between them (be on opposite poles). If so, the neutral wire will carry the difference of currents. (if one is 11A and the other is 13A, the neutral carries 2A). A double-stuff/duplex has both circuits on the same pole, and the neutral current would stack (24A) instead of cancel, overloading the neutral.
Common maintenance shutoff -- the handles must be tied; shutting off one subcircuit must also shut the other one off. Either by using a 2-pole 240V breaker (same as you would for a dryer) or a factory approved handle tie between two single breakers. They don't make handle ties for double-stuffs, so if you respect this rule, the above rule takes care of itself.
Must pigtail neutrals -- you can't have it where removing, say, a receptacle interrupts neutral for the other half-circuit.
These types of circuits have fallen out of favor because they make life very complicated when you bring GFCI or AFCI into the picture.
Best Answer
It looks like feeder wire, probably stranded aluminum—though it could be copper. Judging by the scale of the breakers it looks to be AWG 6 or 4. See this chart for ampacity ratings.
If you inspect the jacket of the wire for up to 18 inches, you should be able to find some writing which gives the exact wire size (gauge number), temperature rating, and voltage rating of the insulator. Also, many cables have a distance number, usually in feet, from some origin (maybe the beginning of the 1000' spool the wire came from).