Not quite.
-4(x+1)-9=12x+11 (you had -12 + 11)
-4x-13=12x+11 (you were right)
Add 13 to each side: (right again)
-4x=12x+24 (you had -12x + 24)
Subtract 12x from each side: (you had +12x)
-16x=24 (you had 8x=24)
Divide through by 8: (right)
-2x=3 (you had x=3 which was because you had 8x=24)
So 2x=-3 and x=-3/2.
Final step: plug the answer into the original equation:
-4(-3/2+1)-9=-4*(-1/2)-9=2-9=-7 = 12*(-3/2)+11=-18+11
So left and right both come to -7, proving the answer x=-3/2.
You do need to be very careful all the time; but if you plug in your answer you can prove whether or not you got it right. If the final step doesn't work out, you must have made a mistake so you go back and check your working carefully. Everyone makes mistakes, so it's a step worth taking to give you confidence.