What are the vertical asymptotes of r(x) = 3x - 3 x2 - 4

They are x = 2 and x = -2.

I assumed since you were looking for vertical asymptotes, you intended to write that the two expressions were being divided.

In this case, the denominator would be x^2 - 4, which can factor into:

(x - 2)(x + 2)

And since the denominator can't be zero, the value of 2 and -2 would make it undefined and you would have vertical asymptotes.