A Direction That Isn't Unit Length

A model's error surface is

$L(x, y) = 4x^2 + xy + y^2$

You are standing at the point $(1,\ 2)$, and you are not free to head in the steepest direction — a constraint forces you to move along the direction of the vector

$\mathbf{v} = (4,\ -3)$

The directional derivative measures how fast $L$ changes per unit of distance travelled.

What is the rate of change of $L$ at $(1,\ 2)$ in the direction of $\mathbf{v}$?