I'm looking for feedback on how to wire a second light from an existing wall switch. I am providing a self-drawn diagram and an actual photo of the existing box with the wires exposed in an attempt to express myself as clearly as possible.
So here are the details. The areas of each corner marked "A", "B", "C" and "D" are actual Romex wires that enter the box from each corner. This will be a two gang junction box, by the way. One will control the existing ceiling fan and the other will be a dimmer for the new lights. Currently, the "A" Romex leads up into the ceiling and powers a ceiling fan. Romex "B" will power the new lights which will have a total of four LED flush-mount lights in the corners of the ceiling. Total wattage for all four will be 28w. The ceiling fan has a total of 57w (that's at the highest settings for both the light and fan speed). Romex "C" (I'm 98% certain) is the power from the circuit box. And Romex "D" is a line that runs to the bathroom. I know that bathrooms should have their own circuit. I didn't wire it that way. That's just how I found it. I can't change that.
What I am looking to learn is how to connect Romex "B" (the new light) correctly. I tried connecting a dimmer switch for my new lights by connecting the the hot wire from Romex "B" to the black shared wires "A" and "D". Then I tried to connect the neutral white wire from Romex "B" to the neutral white shared wires from Romex "A", "C" and "D." This blew the circuit and I fried my dimmer switch.
I think my error was that I connected incorrectly to Romex "D" as and now I'm pretty sure that wire goes to the bathroom (hence why I mentioned I'm 98% certain above). Romex wires "C" and "D" are either one or the other (either power from circuit breaker box or a line to power the bathroom).
Do I connect the Romex "B" hot to the hot on Romex "C" and Romex "B" white neutral to Romex "A", "C" and "D"? I am confused.