The changes in $x$ from one row to the next are $+3\text{,}$$+2\text{,}$ and $+8\text{.}$ That’s not a consistent pattern, but we need to consider rates of change between points. The rate of change between the first two points is $\frac{-8-(-2)}{6-3}=-2\text{.}$ The rate of change between the next two points is $\frac{-12-(-8)}{8-6}=-2\text{.}$ And the rate of change between the last two points is $\frac{-20-(-12)}{12-8}=-2\text{.}$ So the rate of change, $-2\text{,}$ is constant regardless of which pairs we choose. That means these pairs describe a linear relationship.