So you start off with the first two terms which are -4y^3 and 3y^2. Now you must think what numbers could we possibly have that will multiply to them.
Only the factors 4, 1, 3 and 1 work but we cannot ignore the negative. If we were to place the negative in the other set of ( ), the answer would not come out right.
So for now, it should be -(4y-3)(y^2)
So what number will give us -6? Since -3 times something gives us -6, it has to be -2 because once we do the FOIL method and multiply it by the negative, we are not going to get -6 because if it were to be a positive two, it would still give us a negative 6 but since the negative is being multiplied to it, we would receive -6.
So our final answer has to be: -(4y-3)(y^2-2)
