3p+6=4q-12,
3p-4q=-18 ①
(3q+4)/2-(p-5)/6=0, multiply through by 6:
9q+12-p+5=0,
-p+9q=-17, multiply through by 3:
-3p+27q=-51 ②
Add ① and ②:
3p-4q=-18
-3p+27q=-51
23q=-69, q=-3.
Substitute in ① for q:
3p+12=-18,
3p=-30, p=-10.
CHECK
3(p+2)=3(-8)=-24; 4(q-3)=4(-6)=-24✔️
(3q+4)/2-(p-5)/6=(-9+4)/2+15/6=-5/2+5/2=0✔️
ANSWER: p=-10, q=-3.