Let’s the point $(-4,6)$ divide the line segment AB in the ratio k:$1$.
Thus, by using the section formula, we have
$(-4,6)=\left( \frac{3k-6}{k+1},\frac{-8k+10}{k+1} \right)$
$-4=\frac{3k-6}{k+1}$
$-4k-4=3k-6$
$7k=2$
$k:1=2:7$
So the same can be checked for the y-coordinate also.
Thus , the ratio in which the point $(-4,6)$ divides the line segment AB is $2:7$