To solve $6\sqrt{6}(\sqrt{7} + \sqrt{6})$, we apply the distributive property to multiply through:

1. Expand the expression: $6\sqrt{6}(\sqrt{7} + \sqrt{6}) = 6\sqrt{6} \cdot \sqrt{7} + 6\sqrt{6} \cdot \sqrt{6}.$

2. Simplify each term:

   • First term: $6\sqrt{6} \cdot \sqrt{7} = 6\sqrt{42}$ (since $\sqrt{6} \cdot \sqrt{7} = \sqrt{42}$).
   • Second term: $6\sqrt{6} \cdot \sqrt{6} = 6 \cdot 6 = 36$ (since $\sqrt{6} \cdot \sqrt{6} = 6$).

3. Combine the simplified terms: $6\sqrt{42} + 36.$

Thus, the final simplified answer is: $6\sqrt{42} + 36.$

Let me know if you have questions or need further clarifications!

Here are 5 related questions for practice:

1. How would you multiply $5\sqrt{3}(\sqrt{8} + \sqrt{3})$?
2. Simplify $4\sqrt{2}(\sqrt{5} - \sqrt{3})$.
3. What is the result of $\sqrt{6}(\sqrt{10} + \sqrt{15})$?
4. If you distribute $3\sqrt{7}(\sqrt{14} - \sqrt{7})$, what is the result?
5. Can $2\sqrt{10} \cdot \sqrt{5}$ be simplified further?

Tip: When working with square roots, always simplify and combine like terms to make expressions as compact as possible.