12x³-16x²-3x+4

I'll do some coloring:

12x³-16x²-3x+4

Factor 4x² out of the two red terms:

4x²(3x-4)-3x+4

Factor -1 out of the two blue terms:

4x²(3x-4)-1(3x-4)

Now I'll re-color the above:

4x²(3x-4)-1(3x-4)

Now look at the two purple parentheses:

You can take out the entire purple parentheses just
as though it were merely a single number or letter,
and it will leave the two green factors to put
in a parentheses:

(3x-4)(4x²-1)

But this is not finished because the (4x²-1) is
the difference of two perfect squares and factors
as (2x-1)(2x+1), so the final answer is

(3x-4)(2x-1)(2x+1).

or without the coloring:

(3x-4)(2x-1)(2x+1).

Edwin