If the line $x - 1 = 0$ is the directrix of the parabola $y^2 - kx + 8 = 0$, then one of the values of $k$ is

Rewrite the parabola as $$y^2=kx-8=k\left(x-\frac{8}{k}\right).$$ This is of the form $$y^2=4a(x-h),$$ where $$h=\frac{8}{k}$$ and $$4a=k.$$ For such a parabola, the directrix is $$x=h-a.$$ So here the directrix is $$x=\frac{8}{k}-\frac{k}{4}.$$ Given $$x-1=0,$$ we have $$x=1,$$ hence $$\frac{8}{k}-\frac{k}{4}=1.$$ Multiply by $$4k$$ to get $$32-k^2=4k.$$ Thus $$k^2+4k-32=0.$$ Factoring gives $$ (k-4)(k+8)=0. $$ So $$k=4$$ or $$k=-8.$$ Among the given options, the matching value is $$4.$$ Therefore the correct option is $C$.