There are probably some choices we're not being shown, but let's just do the whole procedure.
x² + 6x - 8 = 0
Step one: move the 8 to the other side.
x² + 6x = 8
Step two: add (6/2)²=9 to both sides.
x² + 6x + 3² = 8 + 9
Step three: Factor
(x + 3)² = 17
Step four: take the square root
x + 3 = ±√17
Step five: Solve for x,
x = -3 ± √17