The expression to evaluate is:

$3\sqrt{3} + \sqrt{4} + |\sqrt{3}| + \sqrt[3]{-8}$

Let's break it down step by step:

1. $3\sqrt{3}$: This is $3 \times \sqrt{3}$.
2. $\sqrt{4}$: The square root of 4 is 2.
3. $|\sqrt{3}|$: The absolute value of $\sqrt{3}$ is $\sqrt{3}$.
4. $\sqrt[3]{-8}$: The cube root of -8 is -2.

Now, combine these values:

$3\sqrt{3} + 2 + \sqrt{3} - 2$

Combine like terms:

$3\sqrt{3} + \sqrt{3} = 4\sqrt{3}$

So the expression simplifies to:

$4\sqrt{3}$

Would you like any further details or have any questions?

Here are 5 questions you can ask:

1. How do you simplify expressions with square roots?
2. What is the difference between a square root and a cube root?
3. Can you explain the properties of absolute values?
4. How do you handle operations involving roots and exponents?
5. What are some common mistakes to avoid when working with roots and radicals?

Tip: When simplifying expressions with roots, always look for opportunities to combine like terms and simplify inside the root if possible.