If your at idle for 4 seconds and you increase/rush the throttle, and the engine stops, its a low speed adjustment problem. How many turns out is the low-speed needle value currently from being "seated" A cold engine on a cold day will handle "more sloppy fuel" at idle first time out than it will once it heats up. Thats the definition of a "choke". It sounds like its loading up....

You need to define better how it stops... Lots of smoke? Dies immediately. Staggers like its choking on fuel. And when you hear it staggering, what happens if you immediately ease back on the throttle before it stops...does it suddenly improve?