The expression you've provided is:

$3 \sqrt{6} \left( \sqrt{7} - \sqrt{2} \right)$

To simplify this, let's distribute $3 \sqrt{6}$ to both terms inside the parentheses:

$= 3 \sqrt{6} \times \sqrt{7} - 3 \sqrt{6} \times \sqrt{2}$

We can now multiply the square roots:

$= 3 \sqrt{42} - 3 \sqrt{12}$

Next, simplify $\sqrt{12}$:

$\sqrt{12} = \sqrt{4 \times 3} = 2 \sqrt{3}$

Thus, the expression becomes:

$= 3 \sqrt{42} - 6 \sqrt{3}$

So the final simplified expression is:

$3 \sqrt{42} - 6 \sqrt{3}$

Would you like further clarification on any step or more details?

Here are five related questions to consider:

1. How do you multiply square roots with coefficients?
2. What is the method to simplify a square root like $\sqrt{12}$?
3. Can this expression be simplified further by approximating the square roots numerically?
4. What are some common strategies to handle expressions with multiple square roots?
5. What are the real-world applications of simplifying expressions like this?

Tip: Always look for perfect squares within a square root to simplify expressions effectively.