Answer
$c=8$
Work Step by Step
The coefficient of the middle term of a perfect square trinomial is equal to twice the square root of the third term. Hence, to make the given expression, $
x^2+cx+16
$, a perfect square trinomial, then,
\begin{array}{l}
c=2\sqrt{16}
\\\\
c=2\cdot4
\\\\
c=8
.\end{array}