jmc

To find the intersection, we must find the point satisfying both equations. Hence we must solve the system $$\begin{array}{rl}y& =-4x,\\ y-2& =12x.\end{array}$$Substituting the expression for $y$ in first equation into the second equation, we obtain $-4x-2=12x$. Solving for $x$ we find that $x=-\frac{1}{8}$. Plugging this into the first expression for $y$ above, we find that $y=-4\cdot -\frac{1}{8}=\frac{1}{2}$. So the intersection is $\boxed{\left(-\frac{1}{8},\frac{1}{2}\right)}$.