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^2) - color(red)(x) - color(red)(3))(color(blue)(x^2) + color(blue)(4x) + color(blue)(2))# becomes:
#(color(red)(x^2) xx color(blue)(x^2)) + (color(red)(x^2) xx color(blue)(4x)) + (color(red)(x^2) xx color(blue)(2)) - (color(red)(x) xx color(blue)(x^2)) - (color(red)(x) xx color(blue)(4x)) - (color(red)(x) xx color(blue)(2)) - (color(red)(3) xx color(blue)(x^2)) - (color(red)(3) xx color(blue)(4x)) - (color(red)(3) xx color(blue)(2))#
#x^4 + 4x^3 + 2x^2 - x^3 - 4x^2 - 2x - 3x^2 - 12x - 6#
We can now group and combine like terms:
#x^4 + 4x^3 - x^3 + 2x^2 - 4x^2 - 3x^2 - 2x - 12x - 6#
#x^4 + 4x^3 - 1x^3 + 2x^2 - 4x^2 - 3x^2 - 2x - 12x - 6#
#x^4 + (4 - 1)x^3 + (2 - 4 - 3)x^2 + (- 2 - 12)x - 6#
#x^4 + 3x^3 + (-5)x^2 + (-14)x - 6#
#x^4 + 3x^3 - 5x^2 - 14x - 6#
