To simplify the given radical expression:

$4\sqrt{8} - \sqrt{16} - 2\sqrt{32}$

Step 1: Simplify each square root term.

1. Simplify $\sqrt{8}$: $\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}$ So, $4\sqrt{8} = 4 \cdot 2\sqrt{2} = 8\sqrt{2}$.

2. Simplify $\sqrt{16}$: $\sqrt{16} = 4$

3. Simplify $\sqrt{32}$: $\sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2}$ So, $-2\sqrt{32} = -2 \cdot 4\sqrt{2} = -8\sqrt{2}$.

Step 2: Combine like terms.

The expression becomes: $8\sqrt{2} - 4 - 8\sqrt{2}$

Combine the $\sqrt{2}$ terms: $(8\sqrt{2} - 8\sqrt{2}) - 4 = -4$

Final Answer:

$\boxed{-4}$

Would you like more details or clarification on any step?

Here are 5 related questions to deepen your understanding:

1. How do you simplify $\sqrt{50}$ in terms of its prime factorization?
2. What is the general process to combine radical expressions?
3. How would you simplify an expression like $3\sqrt{18} + 2\sqrt{8}$?
4. Can you explain why $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$?
5. How do you handle radicals when simplifying expressions involving addition and subtraction?

Tip: Always look for perfect square factors when simplifying radicals!