#### Answer

$512$

#### Work Step by Step

We start with the given expression: $(2x)^2y$
We plug in the values for $x$ and $y$: $(2\times4)^2\times8$
The order of operations states that first we perform operations inside grouping symbols, such as parentheses, brackets, and fraction bars. Then, we simplify powers. Then, we multiply and divide from left to right. We use these rules to simplify the expression:
First, we simplify inside the parentheses by multiplying: $8^2\times8$
Next, we simplify powers: $64\times8$
Finally, we multiply: $512$