I have a request for a book.  But the requestor has these condition.  No mold, stains, water damage, writing in the book and also no cracked spines.  I am not sure what they mean by a cracked spine on a paperback book.

I think the best thing to do would to PM the person and ask for a little more detail. What might constitute a "cracked spine" to me might mean something totally different to someone else. I would think an undesirable "cracked spine" would mean that the book has been bent backward harshly and perhaps is in danger of losing pages. But... that's just my opinion.

I'd  PM. If they don't respond, it's their problem... but better to be sure.

when the glue cracks in half and the spine is in two pieces, held together by paper.

That is what most people would mean.

It is always safer to ask someone with an RC like that exactly what they mean, though, if you are not sure.

Generally, a cracked spine is where the pages tend to fall open at a certain part.  Here's a picture of what I consider cracked;

I would turn it down since they could mean just a creased spine (they left it too vague, imo). Unless they gave you a username to contact them by, and you feel inclined to do so, I would decline. Better safe than sorry.