The problem is asking to simplify the expression:

$\frac{8}{3 \sqrt{12}}$

Let's go step by step:

1. Simplify the square root of 12: $\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$

2. Substitute this back into the expression: $\frac{8}{3 \sqrt{12}} = \frac{8}{3 \times 2\sqrt{3}} = \frac{8}{6\sqrt{3}} = \frac{4}{3\sqrt{3}}$

3. Rationalize the denominator by multiplying the numerator and denominator by $\sqrt{3}$: $\frac{4}{3\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{4\sqrt{3}}{3 \times 3} = \frac{4\sqrt{3}}{9}$

Thus, the simplified form of the expression is:

$\frac{4\sqrt{3}}{9}$

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How do you simplify an expression with a square root in the denominator?
2. What is the process for rationalizing a denominator?
3. How do you simplify square roots of non-perfect squares?
4. What happens when you multiply a fraction by a form of 1 (like $\frac{\sqrt{3}}{\sqrt{3}}$)?
5. How do square roots behave under multiplication?

Tip: When simplifying expressions with square roots, look for perfect squares within the radicand to simplify the root first!