In step 1, because you want to find factors that multiply to -8 and add to -2. So the correct factorization is (x-4)(x+2). The student got the minus sign wrong.
(Then in step 3 the x=3 is also very wrong, but that looks more like a typo).
(Also, it should be x-4=0 OR x+2=0, there is no x for which both factors are 0 at the same time!)
