Two lines are perpendicular if the multiplication of their slopes is equal to -1.
Isolating y from the equation:
[tex]\begin{gathered} 4x-2y=-16 \\ 4x-2y+16=0 \\ 4x+16=2y \\ \frac{4x+16}{2}=y \\ \frac{4x}{2}+\frac{16}{2}=y \\ 2x+8=y \end{gathered}[/tex]The slope of this line is 2. Therefore, the slope of the line perpendicular to this one will be:
[tex]\begin{gathered} m\cdot2=-1 \\ m=-\frac{1}{2} \end{gathered}[/tex]