공부하하면서... = (I) study and ... at the same time. *... : do something else

look here=) http://www.koreangrammaticalforms.com/

공부: studying In Korean, when you want to make a verb from a (Sino-) noun, just put 하다 after it. We delete 다 and add 면서... if you want to refer to doing something at the same time.