To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
#(color(red)(2x^2) + color(red)(6x) - color(red)(8))(color(blue)(2x^2) - color(blue)(6x) - color(blue)(3))# becomes:
#(color(red)(2x^2) xx color(blue)(2x^2)) - (color(red)(2x^2) xx color(blue)(6x)) - (color(red)(2x^2) xx color(blue)(3)) + (color(red)(6x) xx color(blue)(2x^2)) - (color(red)(6x) xx color(blue)(6x)) - (color(red)(6x) xx color(blue)(3)) - (color(red)(8) xx color(blue)(2x^2)) - (color(red)(8) xx color(blue)(6x)) + (color(red)(8) xx color(blue)(3))#
#4x^4 - 12x^3 - 6x^2 + 12x^3 -36x^2 - 18x - 16x^2 - 48x + 24#
We can now group and combine like terms:
#4x^4 - 12x^3 + 12x^3 - 6x^2 -36x^2 - 16x^2 - 18x - 48x + 24#
#4x^4 + (-12 + 12)x^3 + (-62 -36 - 16)x^2 + (-18 - 48)x + 24#
#4x^4 + (0)x^3 + (-114)x^2 + (-66)x + 24#
#4x^4 - 114x^2 - 66x + 24#
