You do, indeed, add all the like terms, but, unfortunately, your step 2 doesn't match the original expression, Anonymous!
8x + 4y + 4z - 5x + 2z -8y =
3x + 4y + 4z + 2z -8y combining the x's
3x - 4y + 4z + 2z combining the y's
3x - 4y + 6z combining the z's