To solve the exercise you can find the surface area of a rectangular prism with the given measurements. The formula to find the surface area of a rectangular prism is
[tex]\begin{gathered} SA=2lw+2wh+2lh \\ \text{ Where SA is the surface area}, \\ l\text{ is the length,} \\ w\text{ is the width and} \\ h\text{ is the height of the rectangular prism} \end{gathered}[/tex]
So, in this case, you have
[tex]\begin{gathered} l=16in \\ w=12in \\ h=4in \end{gathered}[/tex][tex]\begin{gathered} SA=2lw+2wh+2lh \\ SA=2(16in)(12in)+2(12in)(4in)+2(16in)(4in) \\ SA=384in^2+96in^2+128in^2 \\ SA=608in^2 \end{gathered}[/tex]
Therefore, to wrap the gift box the department will need 608 square inches of wrapping paper.