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The problem is asking for the simplified form of the following expression:

\[
(-9 \sqrt{2}) \times (4 \sqrt{6})
\]

### Step-by-Step Solution:

1. **Multiply the constants**: 
   \[
   -9 \times 4 = -36
   \]

2. **Multiply the square roots**: 
   \[
   \sqrt{2} \times \sqrt{6} = \sqrt{12}
   \]
   Recall that \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\).

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

4. **Multiply the result from step 1 and the simplified square root**:
   \[
   -36 \times 2\sqrt{3} = -72\sqrt{3}
   \]

So, the simplified form of the expression is:

\[
\boxed{-72 \sqrt{3}}
\]

The correct answer is **B**.

Would you like further details or have any other questions?

### Related Questions:
1. What is the rule for multiplying square roots?
2. How can \(\sqrt{12}\) be simplified in different forms?
3. How do you multiply two terms with square roots and constants?
4. How does multiplying negative and positive constants affect the result?
5. What is the general process for simplifying radical expressions?

### Tip:
When multiplying square roots, combine them under a single square root and simplify before multiplying with constants.

What is this expression in simplified form? 

\((-9\sqrt{2})(4\sqrt{6})\)

Explore the process of simplifying radical expressions by multiplying constants and radicals, including a step-by-step guide on handling negative numbers and simplifying square roots to achieve the simplest form. Ideal for high school students learning algebra.

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