find the derivative at a given point (by definition) x^2-6x-16 at x=-2

by definition, the derivative of f(x) is the limit of
(f(x+h)-f(x))/h
So, plug that in for your function and
f(x+h)-f(x) = (x+h)^2 - 6(x+h) - 16 -(x^2-6x-16)
= x^2+2hx+h^2-6x-6h-16-x^2+6x+16
= 2hx+h^2-6h
Now divide that by h, and you get
(f(x+h)-f(x))/h = 2x+h-6
Take the limit, and df/dx = 2x-6
at x = -2, df/dx = -18

What does df/do mean?

Typo dx