Answer
$172.87^\circ$
Work Step by Step
Given $\vec v_1=<4,6>, \vec v_2=<-3,-6>$, we have
$\vec v_1\cdot\vec v_2=(4)(-3)+(6)(-6)=-48$
and the angle between the two vectors
$\theta=cos^{-1}(\frac{\vec v_1\cdot\vec v_2}{||\vec v_1 || || \vec v_2||})\\ =cos^{-1}\frac{-48}{\sqrt {16+36}\sqrt {9+36}}\\ \approx172.87^\circ$
