I'm really confused about some college credits?

Okay, basically, what I'm trying to figure out is will the community college I'm going to attend allow me to grasp all the general education requirements I'll need in order to transfer to a 4-year school. I'm going to be going CCDC (Community College of District of Columbia) and taking up Liberal Studies with a focus of Journalism. When I read how many credits I'd be able to get, it said I could get 32 credits for one year and 63 credits for two years. I get that part. Now, here's the confusing segment. I looked up one of the schools I'm thinking of transferring to, ASU (Arizona State University). Once admitted, I would be trying to get into the Walter Cronkite school, and I saw something that said I need 80 general education requirements and 40 requirements in the major. If I can only get 32 to 63 credits from the school I'm going to be attending, does that knock me out of having a chance of getting into the school. Or will they let me fulfill the remaining requirements once I get that after the one or two years? Same thing goes for another school I want to transfer too, NCCU (North Carolina Central University). They're saying that I need at least 6 semesters or 9 quarter hours transferable college credit. Again, would I be able to get this after one to two years at CCDC? Thank you!