To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
#(color(red)(x) - color(red)(4))(color(blue)(x^2) - color(blue)(5x) + color(blue)(3))# becomes:
#(color(red)(x) xx color(blue)(x^2)) - (color(red)(x) xx color(blue)(5x)) + (color(red)(x) xx color(blue)(3)) - (color(red)(4) xx color(blue)(x^2)) + (color(red)(4) xx color(blue)(5x)) - (color(red)(4) xx color(blue)(3))#
#x^3 - 5x^2 + 3x - 4x^2 + 20x - 12#
We can now group like terms:
#x^3 - 5x^2 - 4x^2 + 3x + 20x - 12#
We can now combine like terms:
#x^3 + (-5 - 4)x^2 + (3 + 20)x - 12#
#x^3 + (-9)x^2 + 23x - 12#
#x^3 - 9x^2 + 23x - 12#