Meghan reduced the size of a rectangle to a height of 2 inches. What is the new width if it was originally 24 inches wide and 12 inches tall?

The original rectangle had a height of 12 inches and a width of 24 inches, so the ratio of the height to the width is 12/24 = 1/2.

If Meghan reduced the size of the rectangle to a height of 2 inches, the ratio of the new height to the new width would also be 1/2.
Let the new width be x.
Then 2/x = 1/2.
Multiplying both sides of this equation by 2x, we get 2 = x/2.
Multiplying both sides of this equation by 2, we get 4 = x.
So the new width is 4 inches. Answer: \boxed{4 \text{ inches}}.