I don't really have a specific problem to ask about, but I'm having trouble with the concept of the parallel axis theorem. Mainly when using the equation to solve for Ix/Iy, what Ix' and Iy' are equal to.

Just for an example, when calculating Iy of this problem:

And splitting the object into 4 rectangles (two on the left, one center, one right)

The two on the left the Iy' is (1/3)base*height, but the other two it's (1/12)*base*height.

The difference I've been told is that the two on the left touch the Y axis, and then you can use the formula involving 1/3.

I understand that, but I seem to still be getting lost.

So I just have a few questions,

If there is no x and y axis, but there's a x' and y', can I treat x' and y' as normal x and y?

If objects/rectangles are touching the x' and y' axis' can I use the Ix' of (1/3)b*h (for rectangles) or do I still have to use 1/12*b*h?

Does anyone have a good explanation of how to use the parallel axis theorem?

This is all very confusing for me. An explanation would be amazing!

All help is greatly appreciated!