The sum of x^2−3xy−y^2 and 2x^2+5xy−4y^2:
x^2−3xy−y^2 + 2x^2+5xy−4y^2
= 3x^2 + 2xy - 5y^2
From 6x^2−7xy+8y^2 subtract the sum of x^2−3xy−y^2 and 2x^2+5xy−4y^2:
6x^2−7xy+8y^2 - (3x^2 + 2xy - 5y^2)
= 6x^2−7xy+8y^2 - 3x^2 - 2xy + 5y^2
= 3x^2−9xy + 13y^2
Answer
3x^2−9xy + 13y^2