The Carnot cycle is simply the ideal thermodynamic cycle, containing the four basic processes (there are always variants of them...) in any thermodynamic cycle. Learning it is a critical part of the beginning of learning thermodynamic analysis. If you tell us what, specifically, you don't understand about it, maybe we can help...
It just seems hard to comprehend motion of a piston movement and under different conditions not having changes of measurement, (heat or pressure). I don't for a moment doubt it's validity. I think it has more to do with not having a good recall of all terms and definitions of things associated with thermodynamics and the Carnot cycle.
My big fear is that age is beginning to show signs of memory loss and poor comprehension, not that they have ever been all that great.
Just found an area of wiki that has a lot of information about air handling equipment as used in aircraft, not a lot of overlapping systems and not very high pressure, but quite similar to what I am trying to describe.
I have made a little progress in your suggestion about presentation, but am finding it hard to make short statements about things that involve a multiple of actions happening at the same time and having positive and negative values that are conditioning different parts of each system.
I'll try to get a little more done tomorrow.