A line $L: y=m x+3$ meets $y$ - axis at $E(0,3)$ and the arc of the parabola $y^2=16 x, 0 \leq y \leq 6$ at the point $F\left(x_0, y_0\right)$. The tangent to the parabola at $F\left(x_0, y_0\right)$ intersects the $y$-axis at $G\left(0, y_1\right)$. The slope $m$ of the line $L$ is chosen such that the area of the triangle EFG has a local maximum Match List I with List II and select the correct answer using the code given below the lists :