To find the new width of the rectangle after dilation, you can use the formula:
\[ \text{New Width} = \text{Original Width} \times \text{Scale Factor} \]
In this case, the original width is 16 inches and the scale factor is 4:
\[ \text{New Width} = 16 , \text{inches} \times 4 = 64 , \text{inches} \]
So, the width of the dilated rectangle will be 64 inches.