밀다 is pushing something along a surface, and the adverb says how hard or how far: 밀어 그래 그렇게 밀면 돼 "push it, yes, just like that", 길게 밀어서 "push it out long". It is also the bathhouse verb — 등을 밀어주다 is scrubbing someone's back at a jjimjilbang, which is what 자신 있게 밀어줄 수 있어요? is asking about. Applied to a person it turns figurative: 너 형 너무 그렇게 밀고 그러지 마, "don't shove him so hard".