#### Answer

$(b)$

#### Work Step by Step

$f(x)=\left\{\begin{array}{ll}
{x-5,}&{\text{if }x\lt-6}\\
{2x^{2},}&{\text{if }-6\leq x\lt-1}\\
{|x|,}&{\text{if }-1\leq x\lt 10}\\
{3x+1,}&{\text{if }x\geq 10}
\end{array}\right.$
$x=-6\ $ belongs to the interval $\quad -6\leq x\lt-1$
so we calculate its function value with $f(x)=2x^{2}$
... choice $(b)$