I've been breaking it down in various ways myself, as well as watching different people explain and talk about it. There's plenty of ambiguity.

There are methods that imply 6/(2(1+2)) as how to read that, and that comes up with 1.

Another way of explaining it is the slash often ends up with...

　　6
───────
　2 (2+1)

Which is 6/6, which is 1.

The statement is intentionally confusing, meant to be solved different ways by different people.

I think the best way I've heard it described is that this is a grammar problem, not a math problem.