I have 12/3 wire running from the breaker box on a 20 amp breaker that powers a bathroom (2 lights and 2 receptacles). I want to splice into this and run 14/2 wire into the living room to run 6 recessed lights. Is this OK to do?
No you should either use a 20 amp breaker and 20 amp recepticles or if you use a 15 amp breaker then use 14/2 or 14/3 wire. Too heavy of wire creates a fire risk. If your new home was wired to code, this seems quite odd.
No, that is against code. Splicing is not allowed nor can you use a lesser gauge on a circuit. To clarify: splicing exposes otherwise insulated wire. The splice has to be done properly such that no wire is exposed, the splice is hardened and this is achieved using a junction box of NEMA appropriate to the installation conditions. A 20A circuit for a bathroom means there is an exhaust fan since a couple of lamps and receptacles do not normally call for that much. That means the circuit has to be able to support 20A and that means the entire circuit. If you extend the circuit using lesser gauge wire than you downgrade the circuit's ability to handle current. This is a fire risk and is a strict no-no.
No, you can't extend a 20A circuit with 14 G wire. And you can't legally downgrade the existing 12 G wire circuit to a 15 A breaker. And you can't put two wires into a single breaker inside the panel. Fastest solution? Almost all brands of panel offer a two breakers in one slot or high density option. So you can get a new thing that fits in the space of one 15A breaker but has two breakers in it and two connection screws on it. Replace an existing 15A breaker with a high density 15/15 and hook up two 15A circuits. These are also available in unequal configurations - so you could get one that had a 15A and a 20A breaker in the space of a single 'normal' 15 or 20 A breaker. In some brands these high density breakers only fit in certain (closer to the mains connection) spaces - typically the top 15 or 20 breaker spaces. Slower solution. That 15 A breaker that you wanted to put two wires on? Follow the wire from it into the attic, cut it, put in a junction box and splice your new 14 G wire in there. Then again, what else is on that circuit and will 15 A supply it all?