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)(2x) - color(red)(4))(color(blue)(3x^2) + color(blue)(8x) - color(blue)(3))# becomes:
#(color(red)(x^2) xx color(blue)(3x^2)) + (color(red)(x^2) xx color(blue)(8x)) - (color(red)(x^2) xx color(blue)(3)) - (color(red)(2x) xx color(blue)(3x^2)) - (color(red)(2x) xx color(blue)(8x)) + (color(red)(2x) xx color(blue)(3)) - (color(red)(4) xx color(blue)(3x^2)) - (color(red)(4) xx color(blue)(8x)) + (color(red)(4) xx color(blue)(3))#
#3x^4 + 8x^3 - 3x^2 - 6x^3 - 16x^2 + 6x - 12x^2 - 32x + 3#
We can now group and combine like terms:
#3x^4 + 8x^3 - 6x^3 - 3x^2 - 16x^2 - 12x^2 + 6x - 32x + 3#
#3x^4 + (8 - 6)x^3 + (-3 - 16 - 12)x^2 + (6 - 32)x + 3#
#3x^4 + 2x^3 + (-31)x^2 + (-26)x + 3#
#3x^4 + 2x^3 - 31x^2 - 26x + 3#
