"6월 4일인가 말하는 거지" 은/는, these ending particles is used to make verbs modifying nouns like an adjective or adjectival clause. Ex) 울다 (cry) -> 우는 아기 (crying baby) 거 is a spoken style of 것. 것 is a dependent noun which cannot come alone but always with an adjective. It is usually used when we indicate something not specifically but vaguely or abstractly. Ex) 마실 것 something to drink / 먹을 것 something to eat. But, with the structure of ‘-는/은 것이다, 것 is also used to add a bit more affirmative nuance to what s/he states. Ex) (1) 흡연은 건강에 해롭다 (2) 흡연은 건강에 해로운 것이다. We can say both (1) and (2) to mean “Smoking is bad for your health”. Lastly, 지 is a question ending particle, but it is also used in an affirmative or suggestion sentence. So, "6월 4일인가 말하는 거지" could be translated into two. If your friend questioned you, it means “you are talking about June 4 or so, right?” If s/he stated this to give you more information about what s/he had already said, it means “I am talking about June 4 or so.” 순희가 돈을 얼마나 모았는가 아는 사람이 있어요? 순희가 돈을 얼마나 모았는지 아는 사람이 있어요? 가 and 지’s usage in the examples is almost the same. In fact, I hardly find a difference but to my ear, 지 sounds more comfortable and natural.

1. In terms of grammar, it should be "6월 4일을 말하는 거지?". "-ㄴ가" is added because the speaker is not quite sure of the date. In spoken, people don't follow grammar.^^' 2.It means "Does anybody know how much 순희 has saved up?" I think "-ㄴ가"is a bit old-fashioned. Both are the same in meaning, but "-ㄴ지" would be more natural. \^o^/