"나한테 작업거는 거예요?" (Are you flirting with me?) is a relatively new vocabulary widely used among young people and the line was taken from one of tvN's soap operas called "로맨스가 필요해 3" (I need romance Season 3) (Click the image above to check the video)
"작업" itself has multiple meanings such as "work", "operation", "project", depending on the context while "걸다" means "start", "initiate" (although it's not used independently with such meaning).
'작업걸다' as a colloquial expression means "trying to attract/seduce someone", "flirting with someone".
If you watch a lot of Korea drama, you must have heard this expression quite a bit!
To learn other useful vocabulary from this clip from a Korean native speaker, please check out http://www.laughingbeans.com/learn/class/144