The black wire is splice to the output on the speed controller and to the black, fan wire at the other end. The red wire is spliced to the output on the dimmer and to the blue, light wire at the other end. The neutral from the source is spliced in the switch box with the white wire, and to the neutral wire on the ceiling fixture at the other end.
The white wire is wrapped with black tape to identify it as hot. The black wire connects the fan to the speed controller. The red wire connects the light to the dimmer.
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.
This wiring diagram illustrates the connections for dual controls, a speed controller for the fan and a dimmer for the lights. The source is at the controllers and the input of each is spliced to the black source wire with a pigtail. From the controllers, 3-wire cable runs to the ceiling outlet box.