The function f(x) = 1/2x-6 was replaced with f(x+k) = 1/2x-4

You need to find the value of 'x'.
f(x + k) = 1/2x + 2
           = x + 4
        x = -4
Substitute into equation
f(-4 + k) = ((1/2(-4) -6)
k ≤ 8 0r k = -8

Please double check this.
Hope this helps :)

What is your question?