There are two levels of discussion here.

One is about finding a common understanding of what anarchism means, the other about how to achieve it.

To understand what no vertical power structure could look like, you could imagine a friend group going to the park together. Who suggests what will differ and change over time, but no one inherently has any power over another.

If we employ a little fantasy, in a post scarcity society (think Star Trek or The Culture), where any conceivable need and whim can be catered for, there is no reason for misbehaviour or crime, and thus no need for enforcement - this is also anarchist.

As to how we get to such a state of being, I can't say. Traditions, history, and cultural trauma seem unbridgeable in less than several generations, and even then we would need more resources and knowledge than I think humanity could have on this level on the Kardashev scale.