In order to complete this problem (and make it easier on ourselves), we should split it into two parts. Let's start with the first part, #(4x-2x^2)(-4x+3)#. Using FOIL (First, Outsides, Insides, Last), we can simplify this down:

#(4x)(-4x)+(4x)(3)+(-2x^2)(-4x)+(-2x^2)(3)#

#-16x^2+12x+8x^3-6x^2#

We don't need to write this in standard form quite yet as we still have the other half of the equation, #(x-4)^3#. The formula for the multiplication of #(a-b)^3# is #a^3+3a^2b+3ab^2+b^3#. Let's use this as a guideline for our multiplication.

#(x-4)^3#

#x^3+(3)(x^2)(-4)+(3)(x)(-4)^2+(-4)^3#

#x^3-12x^2+48x-64#

Let's now combine our two parts to create one answer:

#-16x^2+12x+8x^3-6x^2-(x^3-12x^2+48x-64)#

#-16x^2+12x+8x^3-6x^2-x^3+12x^2-48x+64#

#8x^3-x^3-16x^2-6x^2+12x^2+12x-48x+64#

#7x^3-10x^2-36x+64#