Given that the circle x² + y² + 2ax + 8y + 16 = 0 touches x - axis. We need to find the value of a.

We know that the value of y on the x - axis is 0.

⇒ x² + (0)² + 2ax + 8(0) + 16 = 0

⇒ x² + 2ax + 16 = 0

The quadratic equation will have similar roots if the circle touches the x - axis.

We know that for the quadratic equation ax² + bx + c = 0 the condition to be satisfied for the equal roots is b² - 4ac = 0

⇒ (2a)² - 4(1)(16) = 0

⇒ 4a² - 64 = 0

⇒ a² = 16

⇒ a = ±4

∴The correct option is (b).