Question: I am doing outdoor landscape lighting. I used the 12 gauge wire but have run short. can I extend it with 14 gauge wire? Need about 20 feet more for the led lights.

Answer: 
It would depend on the transformer size existing distance of the 12 AWG and how many lights were already installed. As a great rule of thumb, never mix wire sizes. Voltage drop on landscaping lights is very important because the voltage is low to begin with. Adding 14AWG at the end of the circuit would not be good for that last light. Think of the future, you might want to add more lights. Don't limit a new installation.
If it's 12v lighting, and you have plenty of 14awg, you can use it by doubling up each connector; running 4 wires instead of 2. That will more than makeup for the increased resistance in the smaller gauge wire. 

OTOH, using the 14 on it's own isn't really dangerous over 20' of lighting-level load, and if you're using LED lights, you likely won't notice the minor voltage drop on lights 20' away from the others.

If your system is AC, check your local regulations or just get more 12AWG.