I'm responding to my own comment, since whoever responded to me saying it wasn't ambiguous deleted the comment as I replied.

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. Mathematicians don't agree.

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.