Which of the following tables shows the correct steps to transform x^2+6x + 8=0

Perhaps the most concise way to factor is by "completing the square" which is how the quadratic formula is derived ...

x^2+6x+8=0 move constant to other side, subtract 8 from both sides

x^2+6x=-8, halve the linear coefficient, square it, then add that to both sides, in this case (6/2) ^2=3^2=9

x^2+6x+9=1 now the left side is a perfect square of the form

(x+3) ^2=1 take the square root of both sides

x+3=±√1 subtract 3 from both sides

x=-3±√1

x=-3±1

x=-4 and - 2

Since the zeros occur when x=-4 and - 2 the factors of the equation are:

(x+2) (x+4)