Which of the following functions' graphs are shifted down 6 units when compared to the parent function f(x) = x? Note that there may be other transformations as well, so the question is whether or not a particular transformation of the parent includes a vertical shift down of 6 units.

A) g(x) = 2(x - 6)

B) g(x) = x/6

C) g(x) = 2(x + 6)

D) g(x) = x - 6

E) g(x) = x + 6

F) g(x) = 3x + 6

G) g(x) = 6x

H) g(x) = 3x - 6