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In the given problem, apply your knowledge in algebraic expression and basic mathematics especially in solving polynomials.

1. Add (2a² - 3bc - 4d) and (-5a² - 10bc + 2d)

(2a² - 3bc - 4d) + (-5a² - 10bc + 2d)

Add the similar terms and consider the integers sign.

2a² + (-5a²) = -3a²

(-3bc) + (-10bc) = -13bc

(-4d) + (2d) = -2d

Answer: -3a² - 13bc - 2d

2. Subtract (2x³ - 6) from (5x + 8)

(2x³ - 6) from (5x + 8) → (5x + 8) - (2x³ - 6)

Consider the zero term and integers sign.

(5x + 8) - (2x³ - 6)

0x³ - 2x³ = - 2x³

5x - 0x = 5x

8 - 6 = 2

Answer: -2x³ + 5x + 2

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