Answer:
This seems to be incomplete because we do not know where g(x) must be tangent to f(x). So i will assume that we want g(x) to be a tangent to f(x) in the point x0.
We know that for a function f(x), f'(x) is the tangent function in at the point x.
Where f'(x) = df(x)/dx
So we can find a value of k that is equal (for some value of x) to the first derivative of f(x).
g(x) = 4*x - k
f(x) = -x^2 + 8*x + 20
f'(x) = -2*x + 8
Now we want to find a value of k such that:
4*x0 - k = -2*x0 + 8
4*x0 - k = -2*x0 + 8
4*x0 + 2*x0 - 8 = k
6*x0 - 8 = k
Then if we want g(x) to be a tangent to f(x) = -x²+8x+20 in the point x0, we must have k = 6*x0 - 8