`{:("Quantity A","Quantity B"),((sqrt6xxsqrt(18))/(sqrt9),(sqrt8xxsqrt(12))/(sqrt6)):}`

Answer

To solve the problem, we need to evaluate the two quantities given:

**Quantity A**: \( \frac{\sqrt{6} \times \sqrt{18}}{\sqrt{9}} \)

**Quantity B**: \( \frac{\sqrt{8} \times \sqrt{12}}{\sqrt{6}} \)

Let's solve each quantity step by step.

### Step 1: Calculate Quantity A

1. **Expression**:
\[ \text{Quantity A} = \frac{\sqrt{6} \times \sqrt{18}}{\sqrt{9}} \]

2. **Simplify \(\sqrt{18}\)**:
\[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2} \]

3. **Substituting back**:
\[ \text{Quantity A} = \frac{\sqrt{6} \times 3\sqrt{2}}{\sqrt{9}} = \frac{3\sqrt{6} \sqrt{2}}{3} \]

4. **Cancel \(3\)**:
\[ \text{Quantity A} = \sqrt{6} \times \sqrt{2} = \sqrt{12} \]

5. **Simplify \(\sqrt{12}\)**:
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]

6. **Approximate \(2\sqrt{3}\)**:
\[ 2\sqrt{3} \approx 2 \times 1.732 = 3.464 \]

### Step 2: Calculate Quantity B

1. **Expression**:
\[ \text{Quantity B} = \frac{\sqrt{8} \times \sqrt{12}}{\sqrt{6}} \]

2. **Simplify \(\sqrt{8}\)**:
\[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2} \]

3. **Simplify \(\sqrt{12}\)**:
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]

4. **Substituting back**:
\[ \text{Quantity B} = \frac{(2\sqrt{2}) \times (2\sqrt{3})}{\sqrt{6}} = \frac{4\sqrt{6}}{\sqrt{6}} \]

5. **Cancel \(\sqrt{6}\)**:
\[ \text{Quantity B} = 4 \]

### Step 3: Compare the Two Quantities

- **Quantity A**: \( \approx 3.464 \)
- **Quantity B**: \( 4 \)

### Conclusion

Since \( 4 > 3.464 \), we conclude that:

**Quantity B is greater than Quantity A.**

---