To determine the scale factor of Ashley's drawing, we need to compare the width of the closet in real life to the width of the closet in the drawing.
The real-life width of the closet is 4 feet. We need to convert this measurement into inches for easier comparison since the drawing's width is given in inches.
1 foot is equal to 12 inches, so:
\[ 4 \text{ feet} = 4 \times 12 \text{ inches} = 48 \text{ inches} \]
Now, the closet in the drawing is 2 inches wide.
Next, we find the scale factor by dividing the width in the drawing by the width in real life:
\[ \text{Scale factor} = \frac{\text{Width in drawing}}{\text{Width in real life}} = \frac{2 \text{ inches}}{48 \text{ inches}} \]
Now we simplify the fraction:
\[ \frac{2}{48} = \frac{1}{24} \]
Thus, the drawing's scale factor is:
\[ \boxed{\frac{1}{24}} \]