How do you factor $ - 6cf + 8{c^2}d - 9df + 12c{d^2}?$

Hint: Factorization is the process of finding which prime numbers can be multiplied together to make the original number. First of all make the pair of two two terms and find out the common factors from both the two pairs and simplify for the resultant required value.

Complete step by step solution:
Take the given expression: $ - 6cf + 8{c^2}d - 9df + 12c{d^2}$
Now, make the pair of two terms in the above equation-
$ = \underline { - 6cf + 8{c^2}d} - \underline {9df + 12c{d^2}} $
Find out the common multiple outside from both the paired terms. When you take out a negative sign outside the bracket then the sign of the other term also changes.
$ = - 2c(3f - 4cd) - 3d(3f - 4cd)$
Take out the multiple common from the above expression.
$ = (3f - 4cd)( - 2c - 3d)$
This is the required solution.
So, the correct answer is “$ (3f - 4cd)( - 2c - 3d)$”.

Note: Prime factorization is the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are the numbers greater than $1$ and which are not the product of any two smaller natural numbers. For Example: $2,{\text{ 3, 5, 7,}}......$ $2$ is the prime number as it can have only a $1$ factor.