To solve the expression \( 4L \ 250ml \times 3L \ 500ml + 6L \ 575ml \), we need to handle the multiplication and addition of quantities in liters and milliliters carefully.

### Step 1: Convert everything to milliliters
We will convert all the liters and milliliters into milliliters for easier calculation. 

- \( 4L \ 250ml \) = \( 4 \times 1000ml + 250ml = 4250ml \)
- \( 3L \ 500ml \) = \( 3 \times 1000ml + 500ml = 3500ml \)
- \( 6L \ 575ml \) = \( 6 \times 1000ml + 575ml = 6575ml \)

### Step 2: Perform the multiplication
Now multiply the first two terms:

\[
4250ml \times 3500ml = 14,875,000 \ ml^2
\]

This result is in \(ml^2\) (square milliliters), which doesn't directly add to milliliters, so if we intend for the operation to be physical quantities like volumes (liters and milliliters), the expression \( \times \) could be representing combining the two volumes instead of multiplying directly.

### Step 3: Add the final term
Since multiplication of volumes in this form isn't meaningful in typical physical contexts, we can reconsider if you're referring to another operation like total combining of volumes instead. Let me know if that's what you intended or clarify your goal for this calculation (is this dimensional calculation etc?)

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This problem involves converting liters to milliliters, multiplying quantities, and adding volumes. The detailed solution provides step-by-step guidance for students in Grades 5-7 to handle unit conversions and understand how to combine and calculate volumes effectively.

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