Factor. \[ z^{2}-8 z+12 \]

Step 1 ：To factor the quadratic equation \(z^{2}-8 z+12\), we need to find two numbers that multiply to 12 (the constant term) and add to -8 (the coefficient of the middle term).

Step 2 ：The numbers that satisfy these conditions are -6 and -2 because \((-6)*(-2) = 12\) and \(-6 + (-2) = -8\).

Step 3 ：Therefore, the factored form of the equation is \((z - 6)(z - 2)\).