Suppose a, b denote the distinct real roots of the quadratic polynomial $x^2+20x-2024$  and suppose c, d denote the distinct complex roots of the quadratic polynomial  $x^2-20x+2024$ .Then the value of $ac(a-c)+ad(a-d)+bc(b-c)+bd(b-d)$  is

Given quadratic polynomials, $x^2+20x-2020$  and  $x^2-20x+2020$ having a, b distinct real and c, d distinct complex roots respectively.
So,   $a+b=-20,ab=-2024$
And   $c+d=20,cd=2024$
Now,  $ac(a-c)+ad(a-d)+bc(b-c)+bd(b-d)$
 $=a^2(c+d)-a(c^2+d^2)+b^2(c+d)-b(c^2+d^2)$
 $=(c+d)(a^2+b^2)-(c^2+d^2)(a+b)$
 $=(c+d)[{(a+b)}^2-2ab]-(a+b)[{(c+d)}^2-2cd]$
 $=20[{\left(20\right)}^2+4048]+20[{\left(20\right)}^2-4048]$
 $=2\times 20\times {\left(20\right)}^2=40\times 400=16000$