Key Concept: If a point lies on a given line (or curve), then the x- and y-coordinates of that point must satisfy the equation of that line (or curve)

So, we can conclude that:
x = a and y = b is a solution to the equation x = 2y + 8
and
x = a–4 and y = b+k is a solution to the equation x = 2y + 8

Let's deal with each case.
If x = a and y = b is a solution to the equation x = 2y + 8, then we can replace x and y with a and b
We get: a = 2b + 8
Rewrite as: a - 2b = 8


If x = a–4 and y = b+k is a solution to the equation x = 2y + 8, then we can replace x and y with a-4 and b+k
We get: a-4 = 2(b+k) + 8
Expand: a - 4 = 2b + 2k + 8
Add 4 to both sides to get: a = 2b + 2k + 12
Subtract 2b from both sides: a - 2b = 2k + 12

We now have two equations:
a - 2b = 2k + 12
a - 2b = 8

Subtract the bottom equation from the top equation to get: 0 = (2k + 12) - 8
Simplify: 0 = 2k + 4
So: -4 = 2k
Solve: k = -2

Answer: B

Cheers,
Brent