To find the missing length of a rectangular prism (also known as a rectangular box), we can use the formula for the surface area of a rectangular prism, which is given by:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
In this case, the width (\( w \)) and height (\( h \)) are both 8 inches, and the surface area is 256 in². Substituting the known values into the formula gives:
\[ 256 = 2(l \cdot 8 + l \cdot 8 + 8 \cdot 8) \]
Next, simplify the equation:
- \( 8 \cdot 8 = 64 \)
- Therefore, the equation becomes: \[ 256 = 2(l \cdot 8 + l \cdot 8 + 64) \] \[ 256 = 2(16l + 64) \] \[ 256 = 32l + 128 \]
Now, subtract 128 from both sides:
\[ 256 - 128 = 32l \] \[ 128 = 32l \]
Next, divide both sides by 32 to solve for \( l \):
\[ l = \frac{128}{32} = 4 \]
Thus, the missing length of the rectangular prism is:
\[ \boxed{4 \text{ inches}} \]