It's all about how far the center point travels. The center point of the coin travels the same distance (2 * Pi * radius) in both scenarios. A more extreme example: if you drove a nail anywhere in the edge of the coin and spun it around, the arrow would be pointing up again, the red line would have a length of 0, but the center still would have traveled 2*Pi*r.
One more analogy. Let x = 6, y =2 and z = (1+2) This would make the equation x/yz. That change in notation may seem irrelevant to non-math/engineer/scientists, but it is very clear in a "science" notation how we would deal with order of operations of those variables (e.g. PV=nRT then T = PV/nR)
I've seen several math polls on facebook over the last year or two, but this is definitely the most confusing example. From a meta-math standpoint this is just bad ergonomics. It's the equivalent of putting handles on a push-only door and wondering why people hurt themselves trying to pull it open.
That said. I believe the answer is 1, and here's why. The notation x(y+z) is a very strong signal for the distributive property of parenthetical math notation such that it is logical to replace 2(1+2) with (2*1+2*2) => 6/(2*1+2*2) = 1. Furthermore, the commutative property of multiplication should be assumed such that 6/2(1+2) = 6/(1+2)2. Again implying that the answer must be 1.
That said. I believe the answer is 1, and here's why. The notation x(y+z) is a very strong signal for the distributive property of parenthetical math notation such that it is logical to replace 2(1+2) with (2*1+2*2) => 6/(2*1+2*2) = 1. Furthermore, the commutative property of multiplication should be assumed such that 6/2(1+2) = 6/(1+2)2. Again implying that the answer must be 1.