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So, it's probably going to seem like a stupid question, but I am curious if one of my units can attack one of my other units.

Only if a special rule causes this to happen. Things like blast weapons scattering back over your own units may cause this, and there's a few psychic abilities that may cause you to target your own units, but you may not voluntarily shoot/assault your own units.

Guys, on the very fist page that question is discussed:
http://www.dakkadakka.com/dakkaforum/posts/list/693702.page

I'm sorry. I looked for an answer using the search function, but obviously I didn't search the right phrase or bother to scroll down and search the old fashioned way. I apologize.

Please delete this thread, it's a constant reminder of my failure as a forum user.

 Heretic Tom wrote:
Please delete this thread, it's a constant reminder of my failure as a forum user.

They do not delete threads, just do not comment and it will go away on its own.