Divide. express the quotient in simplest form.
x^2−x−12/2x^2÷x^2+x−6/2x^3

I strongly urge you to use parentheses here, to remove any ambiguity regarding which quantity is being divided by which quantity.  I'm assuming that you meant

(x^2−x−12)/(2x^2)÷(x^2+x−6)/2x^3.  If that is correct, great.  If not, fix it!  Once correct, you can perform the divisions from left to right, beginning with (x^2-x-12)/2x^2.