To simplify the expression 4x³y² - 8x²y³ + 2x⁴y, we can combine like terms.

First, let's look at the terms with x³. We have 4x³y² and -8x²y³. Since they have the same power of x, we can combine them by adding their coefficients:

4x³y² - 8x²y³ = (4 - 8)x³y² = -4x³y².

Now, let's add the remaining term, 2x⁴y:

-4x³y² + 2x⁴y.

So, the simplified expression is -4x³y² + 2x⁴y.