Answer
parallel.
Work Step by Step
1. Given $\vec v=2i+3j, \vec w=-4i-6j$, we have $\vec v\cdot\vec w=(2)(-4)+(3)(-6)=-26$
2. The angle between the vectors $\theta=cos^{-1}(\frac{\vec v\cdot\vec w}{||\vec v || ||\vec w ||})=cos^{-1}(\frac{-26}{\sqrt {4+9}\sqrt {16+36}})=180^\circ$, thus they are parallel.
