1. **State the problem:** Expand the expression $3(cd-4)(cd+4)$. 2. **Recall the formula:** Use the difference of squares formula: $ (a-b)(a+b) = a^2 - b^2 $. Here, $a = cd$ and $b = 4$. 3. **Apply the formula:** $$ (cd-4)(cd+4) = (cd)^2 - 4^2 = c^2 d^2 - 16 $$ 4. **Multiply by 3:** $$ 3(cd-4)(cd+4) = 3(c^2 d^2 - 16) = 3c^2 d^2 - 48 $$ 5. **Final answer:** $$ \boxed{3c^2 d^2 - 48} $$