I understand part a: f(x)=-4|x-6|+7, but for part b I tried to solve it simultaneously and formed a quadratic equation and then used the discriminant b^2-4ac, and I got m<-28/25, m>28/25, but the answer is -4<m<7/6. Is there an error in my calculations or in the way I solved it?
I would solve it geometrically.
$m$ in $y=mx$ is a line with slope $m$ and it passes through the origin.
I would place my ruler fixed at the origin and rotate it around, we can observe two interesting slope.
If our line is steeper than the line connecting the origin and the vertex, the number of intersection is $0$. Hence find the slope for the line connecting $(0,0)$ and $(6,7)$.
As I further reduce my gradient, it will cut at two places until my line is parallel to the decreasing line. Hence find the slope the line connecting $(6,7)$ and $(9,-5)$.
Our range of interest of $m$ is between the two values.