1. **State the problem:** We need to find the total number of school items being shipped if each box contains $2xy + 3y^2$ items and there are $4x$ boxes. 2. **Write the expression for total items:** Total items = (items per box) $\times$ (number of boxes) = $\left(2xy + 3y^2\right) \times 4x$ 3. **Use distributive property to simplify:** $$4x \times (2xy + 3y^2) = 4x \times 2xy + 4x \times 3y^2$$ 4. **Multiply each term:** $$= 8x^2y + 12xy^2$$ 5. **Final simplified expression:** $$8x^2y + 12xy^2$$ This matches the second option. **Answer:** $8x^2y + 12xy^2$