What is this??

op amp set up with non-inverting gain of 2. To get the full range of 0 to 12V, though, you're going to have to bias the op-amp from somewhat higher than 12V on the Vdd end and somewhat lower than 0V on the Vss end. You could go for a rail-to-rail op-amp - at least that would get you close to the rails without having to change the power supply.

Yes, use an op-amp, PICs may be good for complex applications but for something simple like this you can't beat an op-amp. I think PICs are often over-used these days, people often use them because they don't know how to do it the "propper way".