Final answer:
The given equation simplifies to the linear equation 6y - 8 = 4y + 40, which upon further simplification gives the solution y = 24. The initial answer choices do not match this solution.
Step-by-step explanation:
Solving the Linear Equation
To solve the equation 4y + 2(1y - 4) = 8y - 4(y - 10), first distribute the 2 and the -4 across the parentheses, which gives us 4y + 2y - 8 = 8y - 4y + 40. Combine like terms on both sides to get 6y - 8 = 4y + 40. Next, subtract 4y from both sides and add 8 to both sides to isolate y, resulting in 2y = 48. Finally, divide both sides by 2 to find that y = 24.
Checking the solution, we plug y back into the original equation and verify that both sides are equal. Since the variables cancel out and we are not left with a false statement, this indicates that we have one specific solution for y, which is y = 24.
Therefore, the correct answer is neither (A) nor (B) nor (C) as initially suggested, but rather y = 24.