Answer
$8x^2 - 22xy +12x +15y^2 - 14y - 8$
Work Step by Step
We multiply each term of the first polynomial by each term of the second polynomial. Then we add the products, as follows
$$
(2x- 3y+ 4)(4x - 5y - 2)= 2x(4x - 5y - 2)- 3y(4x - 5y - 2)+ 4(4x - 5y - 2)\\
= 8x^2 - 10xy - 4x- 12yx +15y^2 +6y+ 16x - 20y - 8\\
=8x^2 - 22xy +12x +15y^2 - 14y - 8
.$$
