To simplify the given expression, let's first expand each term:

$(3a - 4)^2 = (3a - 4)(3a - 4) = 9a^2 - 12a - 12a + 16 = 9a^2 - 24a + 16$

$9(a - 2)(a + 2) = 9(a^2 - 4) = 9a^2 - 36$

Now, combine the terms:

$(3a - 4)^2 - 9(a - 2)(a + 2) = (9a^2 - 24a + 16) - (9a^2 - 36)$

$= 9a^2 - 24a + 16 - 9a^2 + 36$

$= -24a + 16 + 36$

$= -24a + 52$

Therefore, $(3a - 4)^2 - 9(a - 2)(a + 2)$ simplifies to $-24a + 52$.