To simplify the given expression $8\sqrt{3} - 3\sqrt{12}$, we proceed step by step:

1. Simplify the second term $-3\sqrt{12}$:

   • Factor $12$ into $4 \times 3$: $\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}$.
   • Substitute $\sqrt{12}$ with $2\sqrt{3}$: $-3\sqrt{12} = -3(2\sqrt{3}) = -6\sqrt{3}$.

2. Combine like terms:

   • The expression now becomes $8\sqrt{3} - 6\sqrt{3}$.
   • Combine the coefficients of $\sqrt{3}$: $(8 - 6)\sqrt{3} = 2\sqrt{3}$.

Final Answer: $2\sqrt{3}$

Let me know if you have any questions or need additional clarification!

Here are some related questions to deepen understanding:

1. How do you factorize radicands in square roots for simplification?
2. Why can you combine terms with the same radical (e.g., $\sqrt{3}$)?
3. How would the process change if the radicals were different (e.g., $\sqrt{3}$ and $\sqrt{5}$)?
4. Can you demonstrate simplifying $5\sqrt{18} + 2\sqrt{8}$?
5. What are the key rules for combining or simplifying radical expressions?

Tip: Always factorize the radicand (the number under the square root) completely to identify perfect squares for simplification.