First, we can rewrite this expression as:
#(color(red)(b^2) - color(red)(4b) + color(red)(6))(color(blue)(b^2) - color(blue)(4b) + color(blue)(6))#
To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
#(color(red)(b^2) xx color(blue)(b^2)) - (color(red)(b^2) xx color(blue)(4b)) + (color(red)(b^2) xx color(blue)(6)) - (color(red)(4b) xx color(blue)(b^2)) + (color(red)(4b) xx color(blue)(4b)) - (color(red)(4b) xx color(blue)(6)) + (color(red)(6) xx color(blue)(b^2)) - (color(red)(6) xx color(blue)(4b)) + (color(red)(6) xx color(blue)(6))#
#b^4 - 4b^3 + 6b^2 - 4b^3 + 16b^2 - 24b + 6b^2 - 24b + 36#
We can now group and combine like terms:
#b^4 - 4b^3 - 4b^3 + 6b^2 + 16b^2 + 6b^2 - 24b - 24b + 36#
#b^4 + (-4 - 4)b^3 + (6 + 16 + 6)b^2 + (-24 - 24)b + 36#
#b^4 - 8b^3 + 28b^2 - 48b + 36#