Explanation:
Find min/max value using x = (-b/2a). if a is positive your looking for minimum of a is negative your looking for maximum. Value Guide ax^2+bx+c
x = (-(-8)/2(-4))
x = (8/-8) = -1
Put negative one in the equation
f(-1) = -4(-1)^2-8(-1)-6
f(-1) = -4+8-6 = -2
The range would be (-(infi),-2)
If you are required to solve the equation using derivatives say so in the comments and I will repost using that method.