1. The problem is to find the conjugate of the expression $$-3 + 8\sqrt{6}$$. 2. The conjugate of a binomial expression of the form $$a + b$$ is $$a - b$$. 3. Here, $$a = -3$$ and $$b = 8\sqrt{6}$$. 4. Therefore, the conjugate is $$-3 - 8\sqrt{6}$$. 5. The conjugate simply changes the sign between the two terms. Final answer: $$-3 - 8\sqrt{6}$$