Here, volume of two shapes doesn't relate with each other, so if one has double dimensions than the other, then it's volume won't be exactly double than the other, 'cause they formula's are very different.
Volume of a Cylinder = πr²h
v = π(4)²(6)
v = 96π
Volume of a cone = 1/3 πr²h
v = 1/3 π (8)²(12)
v = 256π
So, Ratio = 256π/96π = 128/48 = 64/24 = 32/12 = 16/6 = 8/3 [ Not 2 ]
In short, She is Incorrect!
Hope this helps!