You are multiplying a 3x3 matrix by a 3x1 matrix
-5 -3 -6 -4
-5 1 8 * 6 =
-8 7 -6 4
(-5)(-4) + (-3)(6) + (-6)(4) = 20-18-24 = -22 = x
(-5)(-4) + (1)(6) + (8)(4) = 20+6+32 = 58 = y
(-8)(-4) + (7)(6) + (-6)(4) = 32+42-24 = 50 = z