f(x) varies directly with x, so this means f(x) = k*x where k is some fixed number. We're told that x = 6 an f(x) = -12 pair up together. So that means we go from
f(x) = k*x
to
-12 = k*6
after we perform two substitutions or replacements. Now solve for k. To do so, divide both sides by 6 like so
-12 = k*6
-12/6 = k*6/6
-2 = k
k = -2
So we can update f(x) = k*x into f(x) = -2*x which is the same as f(x) = -2x
Therefore the answer is choice A