Interview after being fired?

Okay so I'm hoping that someone on here can help me.

I recently just got a call back for a CNA position from a nursing home connected to a very well-known hospital in my area. I'm really excited because this is the first job I will have since I've finished my classes for a program. :)

On the preferred qualifications on the application, it says that they're preferring to have someone that has 6 months of experience in some type of healthcare facility.

I worked for an assisted living facility as an NAR for 6 months, and gave my two weeks. (he next morning after I wrote that, however, I got a call from my boss saying I was terminated since I didn't have my NAC in the allotted amount of time, which they never specified. Needless to say, I left on not so good terms.

I interviewed with another place a week ago with that facility on my resume, and after signing a waiver for them to contact my previous workplaces, I never got a call back, meaning I didn't get the job. I really need this, so I left them off my resume for this interview, but without that job on my application, I only have about 3 months of experience (from another SNF that I worked at after that fiasco). With it, I have 9 months.

My question is, how do I mention those 6 months that I worked at that assisted living facility? Do I even mention it? I mean, it's a long time to be with a facility, especially when you're just starting out. I really need this job and I'm super nervous about what to say and how to say it.

It's been a while since I've interviewed, so could someone give me some tips on that too?