The problem asks us to factor the linear expression $6y - 24$. We need to find an expression that is equivalent to $6y - 24$ from the given options: $3(2y - 8)$, $6(y - 4)$, $6(y + 4)$, and $6y(1 - 4)$.

1. Problem Description

The problem asks us to factor the linear expression $6y - 24$. We need to find an expression that is equivalent to $6y - 24$ from the given options: $3(2y - 8)$, $6(y - 4)$, $6(y + 4)$, and $6y(1 - 4)$.

2. Solution Steps

First, let's analyze the given expression $6y - 24$. We can factor out the greatest common factor (GCF) of the coefficients. The GCF of 6 and 24 is

6.

Factoring out 6 from the expression $6y - 24$, we get:

$6(y - 4)$

Now, let's check the given options:

Option 1: $3(2y - 8) = 6y - 24$. This is equivalent to the given expression.

Option 2: $6(y - 4) = 6y - 24$. This is also equivalent to the given expression.

Option 3: $6(y + 4) = 6y + 24$. This is not equivalent to the given expression.

Option 4: $6y(1 - 4) = 6y(-3) = -18y$. This is not equivalent to the given expression.

Since we are looking for the factored form, we can see that $6(y-4)$ is the most direct factored form. Also, $3(2y-8)$ can be further factored as $3(2(y-4)) = 6(y-4)$. Therefore, the correct answer is $6(y - 4)$.

3. Final Answer

$6(y - 4)$