Explanation

(b)
Given that, $y = 2x + c$ …(i)
And $x^{2} + y^{2} = 16$ …(ii)
We know that, if $y = mx + c$ is tangent to the circle
$x^{2} + y^{2} = a^{2}$, then $c = \pm a\sqrt{1 + m^{2}}$, here, $m = 2,\ a = 4$
$\therefore\ c = \pm 4\sqrt{1 + 2^{2}} = \pm 4\sqrt{5}$