To find the volume \( V \) of a cylinder, you can use the formula:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
Given that the diameter of the cylinder is 8 inches, the radius \( r \) is half of the diameter:
\[ r = \frac{8}{2} = 4 \text{ inches} \]
The height \( h \) of the cylinder is given as 12 inches.
Now, substituting the values into the volume formula:
\[ V = 3.14 \times (4)^2 \times 12 \]
Calculating \( (4)^2 \):
\[ (4)^2 = 16 \]
Now, substituting back into the volume formula:
\[ V = 3.14 \times 16 \times 12 \]
Calculating \( 16 \times 12 \):
\[ 16 \times 12 = 192 \]
Now, substituting back:
\[ V = 3.14 \times 192 \]
Now, performing the multiplication:
\[ V = 602.88 \]
Thus, the volume of the cylinder is
\[ \boxed{602.88} \text{ cubic inches.} \]