If the polynomial 6x6 – 4x5 + 9x – 6 is to be factored by grouping, which step should be taken?

I think you're trying to say 6x^6-4x^5+9x-6. ^ Is a symbol that means the number after it is an exponent.
First step, find the gcf (greatest common factor) between the first two parts. The gcf of 6x^6-4x^5 is 2x^5.
Now take it out. You get
2x^5(3x-2)
If you expand that equation, you will get 6x^6-4x^5 which is why you know it's correct.
Now do the same for the second half.
The gcf for the second two parts is 3.
3(3x-2)
Notice anything? Yep, in both of them, after you take out the gcf, you get (3x-2)
Now, you combine them into one equation
2x^5(3x-2)+3(3x-2)
Then you do this
(2x^5+3)(3x-2)
That's your factored form.