To find the width in boxes of the new drawing with a scale of 1 box = 2 inches, we first need to determine the current width in inches.
The width of the rectangle in the drawing is 3 boxes. Given the scale of 1 box = 4 inches, we calculate the current width:
\[ \text{Current width in inches} = 3 , \text{boxes} \times 4 , \text{inches/box} = 12 , \text{inches} \]
Now, we want to convert this width to the new scale of 1 box = 2 inches. We can find the new width in boxes by dividing the width in inches by the new scale:
\[ \text{New width in boxes} = \frac{12 , \text{inches}}{2 , \text{inches/box}} = 6 , \text{boxes} \]
Therefore, the width in boxes of the new drawing will be 6.