To convert the width from the original scale to the new scale, we first need to determine the actual width of the rectangle in inches at the original scale.
Given that the width in the drawing is 3 boxes, and the scale is 1 box = 4 inches, the actual width is: \[ 3 \text{ boxes} \times 4 \text{ inches/box} = 12 \text{ inches} \]
Now, we need to convert this actual width to boxes at the new scale of 1 box = 2 inches. To do that, we divide the actual width in inches by the new scale: \[ \frac{12 \text{ inches}}{2 \text{ inches/box}} = 6 \text{ boxes} \]
So, the width in boxes of the new drawing will be 6.