jmc

First, we can find the slope of the line through these two points. The slope will be equal to: $$\frac{y_2-y_1}{x_2-x_1}=\frac{-2-6}{-4-(-2)}=\frac{-8}{-2}=4$$ Therefore, the line will have the form $y=4x+b$. To solve for $b$, substitute in one of the given points for $x$ and $y$ as shown: $$\begin{array}{rl}6& =4(-2)+b\\ \Rightarrow 6& =-8+b\\ \Rightarrow 14& =b\end{array}$$ Since $b$ in a line of the form $y=mx+b$ is the $y$-intercept, and this is what we are trying to find, the answer is $\boxed{14}$.