Answer
$\textbf{r} = \langle -3,4,6\rangle + t\langle8,-5,-6 \rangle$
Work Step by Step
Equation of a Line: $\textbf{r} = \textbf{r}_0 + t\textbf{v}$
$\textbf{r}_0 = \langle -3,4,6\rangle$
Given the two points, we can find $\textbf{v}$:
$\textbf{v} = \langle5+3, -1-4, 0-6\rangle = \langle 8,-5,-6\rangle$
$\textbf{r} = \langle -3,4,6\rangle + t\langle8,-5,-6 \rangle$