NEW A3 1.6 engine performance upgrade?

12bhp is very possible but not by that lol

Full system exhaust, manifold, air intake and remap will see maybe more than 12bhp - but not worth it on a 1.6 car that weighs 1.5T
 
It's probably a simple resistor mod which fools the ecu into thinking it's colder than it really is which results in extra fuelling. The extra 12bhp comes from what the engine puts out as standard (Audi usually understate output) and these muppets claiming it's as a result of their resistor mod. I can sell you the2p resistor for £20 if you like ;-)

Most normally aspirated cars will struggle to make 10-15 bhp after a full blown remap as there is so little you can do to improve things (timing, fuelling, throttle response). Turbos are much easier to remap to get big gains.