Explanation

(b)
Slope of the line segment joining $( - 4,\ 6)$ and (8, 8) is
$\frac{8 - 6}{8 + 4} = \frac{2}{12} = \frac{1}{6}$
$\therefore$ Slope of line perpendicular to it.
$m = - \frac{1}{1/6} = - 6$
As the line bisecting it.
$\therefore Mid\ point\ of\ this\ line\ is\ \left( \frac{8 - 4}{2},\frac{8 + 6}{2} \right) = (2,\ 7)$
$\therefore\$Required equation is
$y - 7 = - 6(x - 2)$
$\Rightarrow \ y + 6x - 19 = 0$