Answer
$(d)$
Work Step by Step
Let us solve the given problem in the following way:
$a^2-a-12=0$
or, $a^2-4a+3a-12=0$
or, $(a+3)(a-4)=0$
This can be written as : $a+3=0$ or, $a-4=0$
Thus, $a=-3,4$
Hence, the final answer will be $(d)$.