1. **State the problem:** Simplify the expression $$(a^2 - b^2)(2b - 6a)$$. 2. **Recall the formula:** The expression $a^2 - b^2$ is a difference of squares, which factors as $$a^2 - b^2 = (a - b)(a + b)$$. 3. **Apply the factorization:** Rewrite the expression as $$ (a - b)(a + b)(2b - 6a) $$. 4. **Factor out common terms in the second parenthesis:** $$2b - 6a = 2(b - 3a)$$. 5. **Substitute back:** The expression becomes $$ (a - b)(a + b) \times 2(b - 3a) $$. 6. **Rearrange the factors:** $$ 2 (a - b)(a + b)(b - 3a) $$. 7. **Final simplified form:** $$\boxed{2 (a - b)(a + b)(b - 3a)}$$. This is the fully factored form of the original expression.