To find the area of the dilated rectangle, we start by calculating the area of the original rectangle.
The area \( A \) of a rectangle can be calculated using the formula:
\[ A = \text{height} \times \text{base} \]
For the original rectangle:
\[ \text{height} = 6 \text{ inches} \] \[ \text{base} = 8 \text{ inches} \]
So the area of the original rectangle is:
\[ A = 6 \times 8 = 48 \text{ square inches} \]
Next, we apply the dilation using a scale factor of \( 0.5 \). When a rectangle is dilated, both its height and base are multiplied by the scale factor.
Calculating the new dimensions after dilation:
\[ \text{New height} = 6 \times 0.5 = 3 \text{ inches} \] \[ \text{New base} = 8 \times 0.5 = 4 \text{ inches} \]
Now, we calculate the area of the dilated rectangle using its new dimensions:
\[ \text{Area of the dilated rectangle} = \text{new height} \times \text{new base} = 3 \times 4 = 12 \text{ square inches} \]
Thus, the area of the dilated rectangle is:
\[ \boxed{12} \text{ square inches} \]