We can simplify the expression $\sqrt{8} + S\sqrt{2} - 6\sqrt{2}$.

Step 1: Simplify $\sqrt{8}$

We know that: $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$

Step 2: Combine Like Terms

Now, substitute $\sqrt{8}$ with $2\sqrt{2}$: $2\sqrt{2} + S\sqrt{2} - 6\sqrt{2}$

Combine the terms involving $\sqrt{2}$: $(2 + S - 6)\sqrt{2}$ $(S - 4)\sqrt{2}$

The simplified result is: $(S - 4)\sqrt{2}$

This is the final simplified expression in terms of $S$. If you have a specific value for $S$, you can substitute it to get a numerical result.

Would you like further details or clarification on any part of this?

Here are five related questions:

1. What are the properties of square roots that can simplify expressions?
2. How do you combine like terms involving radicals?
3. How do you solve equations involving radicals?
4. Can $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ be applied in all cases?
5. How do you rationalize a denominator with square roots?

Tip: Always simplify square roots by factoring under the radical sign to find perfect squares.