Factor the trinomial. \[ w^{2}-6 w x+8 x^{2} \]

Step 1 ：To factor the trinomial \(w^{2}-6 w x+8 x^{2}\), we need to find two numbers that multiply to 8 (the coefficient of \(x^{2}\)) and add to -6 (the coefficient of \(w x\)).

Step 2 ：The numbers that satisfy these conditions are -2 and -4.

Step 3 ：Therefore, we can write the trinomial as: \(w^{2}-6 w x+8 x^{2} = (w - 2x)(w - 4x)\).

Step 4 ：\(\boxed{(w - 2x)(w - 4x)}\) is the factored form of the trinomial \(w^{2}-6 w x+8 x^{2}\).