In order to factor this binomial, we need to find the common factors between each term.
Looking at the terms, we can see that each one has the factor 6ad^2.
Therefore, after factoring 6ad^2 from each term, we have:
![\begin{gathered} 12a^3d^2−6ad^3\\ \\ =6ad^2((12a^3d^2−6ad^(3.))/(6ad^2))\\ \\ =6ad^2(2a^2-d) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/fgy8j6snv602x54wsjbbytnoj21a3d0zjr.png)
Therefore the correct option is the fourth one: 6ad^2(2a^2 − d)