Without rephrasing it… I determined that Ann is 16.

I'm not sure why it needs rephrasing—it seems pretty straightforward? What am I missing?

16 works (as another pointed out). Ann is 16 and Mary would have been that age 8 years ago—when of course Ann would then have been 8 (Mary, at 16, was twice her age).

Ah, that makes sense. I originally read it differently.

> Mary is 24 years old. She is twice as old as Ann was when Mary was as old as Ann is now. How old is Ann?

Which I read as:

> Mary is 24 years old. When Mary was Ann's current age, Anne was half the age she currently is.

Which would mean Anne is 16 (because when Mary was 24-8=16, Anne's current age, then Anne was 16/2=8, half Anne's current age).

But re-reading it, then for that to be true the original would have needed to be phrased:

> Mary is 24 years old. She was twice as old as Ann was when Mary was as old as Ann is now. How old is Ann?

> This makes it a bit easier to realize that Ann’s age has to be right in the middle of 12 and 24.

How did you actually make that deduction? I can only see it by writing down an equation. I can't see anything in the problem that directly implies it.

I figured it out by knowing that Ann had to be 12 in the past since Mary is 24 now which is twice Ann’s age. 6 years have passed since Ann was 12 and Mary was 18 making them 18 and 24, respectively.