To solve this inequality, we need to expand and simplify both sides of the inequality.

Expanding the left side:
(x - 2)^2 = x^2 - 4x + 4

Expanding the right side:
x(x - 4) = x^2 - 4x

Now, the inequality becomes:
x^2 - 4x + 4 > x^2 - 4x

Subtract x^2 and add 4x to both sides:
4 > 0

Since 4 is always greater than 0, the inequality x^2 - 4x + 4 > x^2 - 4x is true for all real numbers x.

Therefore, the solution to the inequality (x - 2)^2 > x(x - 4) is all real numbers x.