6x2+x-12=(3x-4)(2x+3); 3x2+14x-24=(3x-4)(x+6).
(6x2+x-12)/(3x2+14x-24)=(2x+3)/(x+6) provided 3x-4≠0, that is, x≠4/3 (x=4/3 leads to a hole).
Also x+6≠0, that is, x≠-6 (x=6 leads to an asymptote).
So the restrictions on the domain is that x is neither 4/3 or -6.