To find the surface area \( S \) of a rectangular prism, you can use the formula:
\[ S = 2(lw + lh + wh) \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given the dimensions:
- Length \( l = 16 \) inches,
- Width \( w = 8 \) inches,
- Height \( h = 4 \) inches.
First, calculate the areas of the three pairs of faces:
- \( lw = 16 \times 8 = 128 \) square inches
- \( lh = 16 \times 4 = 64 \) square inches
- \( wh = 8 \times 4 = 32 \) square inches
Next, sum these areas:
\[ lw + lh + wh = 128 + 64 + 32 = 224 \text{ square inches} \]
Now, substitute this sum into the surface area formula:
\[ S = 2(224) = 448 \text{ square inches} \]
Thus, the surface area of the rectangular prism is \( \boxed{448} \) square inches.