Multiply 4 by each term inside the parentheses: once by $2y$ and once by $-3$.

After you distribute, you will have a term with $y$ and some constant numbers. Combine the constant numbers, paying close attention to their signs (positive/negative).

In Desmos, type f(y) = 4(2y - 3) + 5. This will let you quickly evaluate the original expression for different values of $y$.

Pick a simple value, such as $y = 1$, and type f(1) to see the numeric result of the original expression. Note that value.

For each option, create a function in Desmos, for example A(y) = 8y - 7, B(y) = 8y + 7, etc. Then evaluate each at $y = 1$ (for example, A(1), B(1), etc.) and see which one matches the value of f(1).

To be sure, test another value like $y = 2$ or $y = -1$ and compare f(2) or f(-1) with the values from each answer choice. The expression that matches the original for both values is the equivalent one.

Start with the expression $4(2y - 3) + 5$.

Use the distributive property: multiply 4 by each term inside the parentheses:

• $4 \cdot 2y$
• $4 \cdot (-3)$

So $4(2y - 3)$ becomes $4 \cdot 2y + 4 \cdot (-3)$.

Now simplify each product:

• $4 \cdot 2y = 8y$
• $4 \cdot (-3) = -12$

So $4(2y - 3)$ becomes $8y - 12$.

The whole expression is now $8y - 12 + 5$.

Combine the constant terms $-12$ and $+5$:

So the constant terms combine to $-7$.

From the simplification, $4(2y - 3) + 5$ is equivalent to $8y - 7$.

So the correct choice is $8y - 7$.