The given ratio problem requires verification of the proportion 3:4::6:8. This type of problem tests understanding of the concept of proportion, which states that two ratios are equal.

The proportion 3:4::6:8 means that the ratio of 3 to 4 is the same as the ratio of 6 to 8. In mathematical terms, this can be understood as:

• If \frac{a}{b} = \frac{c}{d}, then the proportion is true.
• Alternatively, we use the cross-multiplication property, which states that for the ratios to be equal, the cross products must be equal. This means:

Cross-multiplication of the terms gives us:

• 3 x 8 = 24
• 6 x 4 = 24

Since both cross products are equal, the given proportion is verified correctly.

Now, let's evaluate the options:

1. 3 \times 8 = 6 \times 4 : This is true, as both sides equal 24.
2. 3 - 4 = 6 - 8 : This simplifies to -1 = -2, which is false.
3. 3 + 8 = 6 + 4 : This simplifies to 11 = 10, which is false.
4. \frac{3}{8} = \frac{6}{4}: This is false because \frac{3}{8} is not equal to \frac{3}{2}.

Thus, the correct option that verifies the proportion is 3 x 8 = 6 x 4.

Conclusion: In verifying proportions, cross-multiplication is a reliable method to determine the equality of two ratios.