we have that
point A(-7,2) and point B(-1,-4)
Step 1
find the distance AB
d=√[(-4-2)²+(-1+7)²]------------> √[36+36]
d=√72
step 2
find the point M
five-sixths of the distance from AB----------> (5/6)*√72
see the attached figure
AC/AB=x/((5/6)*AB)
6/(AB)=x/((5/6)*AB)--------> 6=6x/5
x=30/6-------> x=5
CB/AB=y/((5/6)*AB)
6/AB=y/((5/6)*AB)---------> 6=6y/5
y=30/6-------> y=5
therefore
the coordinate x of point M is
A(-7,2)
Mx=-7+5=-2
the coordinate y of point M is
A(-7,2)
My=2-5=-3
the point M is (-2,-3)