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To interpret the equation \( \frac{x}{8} = \frac{3(x+4)}{2} \) and identify which expression represents a product, let's look at the options provided:
1. **\( \frac{x}{8} \)**: This is a fraction, not a product.
2. **\( \frac{3(x+4)}{2} \)**: This is also a fraction. However, within this expression, \( 3(x+4) \) does represent a product because it is 3 multiplied by the expression \( (x+4) \).
3. **2**: This is just a number and does not represent a product.
4. **\( 3(x+4) \)**: This is indeed a product as it involves the multiplication of 3 with the expression \( (x+4) \).
Based on this analysis, the expression that represents a product is:
**\( 3(x+4) \)**.