Here 3-wire cable is run from a double-pole circuit breaker and split to supply 120 volts to two sets of receptacles. The neutral wire from the circuit is shared by both. This wiring is commonly used in a 20amp kitchen circuit where two appliance feeds are needed, such as for a refrigerator and a microwave in the same location.
The hot source is spliced to the black, fan wire and the black wire running to the dimmer. At the other end, the black cable wire is spliced to one of the hot dimmer wires, it doesn’t matter which one. The other dimmer wire is spliced to the red wire in the switch box which is spliced to the blue, light wire at the other end.
To wire a 3-way switch circuit that controls both the fan and the light, use this diagram. As with all 3-way circuits, the common on one switch is connected to the hot source wire from the circuit. The common on the second 3-way switch is connected to the hot wires on the fan/light.
This diagram shows two switches in the same box with two separate 120 volt sources. Three-wire cable is supplying the source for both switches with the black and red wires going to the bottom switch terminals. The black wire from each light is connected to the top terminal of their respective switch. The white and ground wires are spliced to run to each light fixture.