To find the missing length of a rectangular prism, we can use the formula for surface area. The formula for the surface area \( S \) of a rectangular prism is:
\[ S = 2(lw + lh + wh) \]
where \( l \), \( w \), and \( h \) are the length, width, and height of the prism, respectively.
In this problem, we know the following:
- Height \( h = 8 \) cm
- Width \( w = 8 \) cm
- Surface area \( S = 432 \) cm²
We need to find the length \( l \).
Substituting the known values into the surface area formula:
\[ 432 = 2(l \cdot 8 + l \cdot 8 + 8 \cdot 8) \]
Now simplify inside the parentheses:
\[ 432 = 2(8l + 8l + 64) \] \[ 432 = 2(16l + 64) \] \[ 432 = 32l + 128 \]
Next, subtract 128 from both sides:
\[ 432 - 128 = 32l \] \[ 304 = 32l \]
Now, divide both sides by 32 to solve for \( l \):
\[ l = \frac{304}{32} = 9.5 \]
Thus, the missing length of the rectangular prism is:
\[ \boxed{9.5} \text{ cm} \]