jmc

Lines that are parallel have the same slope. In this case, $AB$ has a slope of $(0-(-4))/(-4-0)=-1.$ This now must be the slope for $XY$. Now we can use the equation $y_2-y_1=m(x_2-x_1)$ to find the value of $k$. Plugging in the coordinates for $Y$ and $X$ we find that $k-8=-1(14-0)$, thus $k=-14+8=-6$. We also could see that from $(0,8)$ to $(14,k)$ we are moving 14 units right, so we also must move 14 units down to get a slope of $-14/14=-1$. Moving 14 units down from $(0,8)$ lands us at $(0,8-14)$ or $(0,-6)$, so $k=\boxed{-6}$.