Ok, to start, let's look at the terms given in this trinomial: 6x^2, -12x, and 9.
Now, let's try to find the greatest common factor of the three terms, which would be 3. One way to do this would be to take each term and break it down using prime factorization, which would look like this:
6x^2= 2*3*x*x
-12x= -1*3*2*2*x
9= 3*3
When you look at the numbers when they are broken down, they all seem to share one factor, which is 3. This would be the greatest common factor you would factor out of the trinomial, and when you do so it should look like this
3(2x^2-4x+3) which would be your answer