$\frac{4 - a}{8a^3} * \frac{12a^5}{a^2 - 16} = \frac{4 - a}{2} * \frac{3a^2}{(a - 4)(a + 4)} = -\frac{a - 4}{2} * \frac{3a^2}{(a - 4)(a + 4)} = -\frac{1}{2} * \frac{3a^2}{a + 4} = -\frac{3a^2}{2(a + 4)}$

$\frac{4c - d}{c^2 + cd} * \frac{2c^2 - 2d^2}{4c^2 - cd} = \frac{4c - d}{c(c + d)} * \frac{2(c^2 - d^2)}{c(4c - d)} = \frac{1}{c(c + d)} * \frac{2(c - d)(c + d)}{c} = \frac{1}{c} * \frac{2(c - d)}{c} = \frac{2(c - d)}{c^2}$

$\frac{b^2 - 6b + 9}{b^2 - 3b + 9} * \frac{b^3 + 27}{5b - 15} = \frac{(b - 3)^2}{b^2 - 3b + 9} * \frac{(b + 3)(b^2 - 3b + 9)}{5(b - 3)} = \frac{b - 3}{1} * \frac{b + 3}{5} = \frac{b^2 - 9}{5}$

$\frac{a^3 - 16a}{3a^2b} * \frac{12ab^2}{4a + 16} = \frac{a(a^2 - 16)}{a} * \frac{4b}{4(a + 4)} = \frac{(a - 4)(a + 4)}{1} * \frac{b}{a + 4} = \frac{a - 4}{1} * \frac{b}{1} = b(a - 4)$

$\frac{a^3 + b^3}{a^2 - b^2} * \frac{7a - 7b}{a^2 - ab + b^2} = \frac{(a + b)(a^2 - ab + b^2)}{(a - b)(a + b)} * \frac{7(a - b)}{a^2 - ab + b^2} = \frac{1}{1} * \frac{7}{1} = 7$

$\frac{x^2 - 9}{x + y} * \frac{5x + 5y}{x^2 - 3x} = \frac{(x - 3)(x + 3)}{x + y} * \frac{5(x + y)}{x(x - 3)} = \frac{x + 3}{1} * \frac{5}{x} = \frac{5(x + 3)}{x}$

$\frac{m + 2n}{2 - 3m} : \frac{m^2 + 4mn + 4n^2}{3m^2 - 2m} = \frac{m + 2n}{2 - 3m} : \frac{(m + 2n)^2}{m(3m - 2)} = -\frac{m + 2n}{3m - 2n} * \frac{m(3m - 2)}{(m + 2n)^2} = -\frac{1}{1} * \frac{m}{m + 2n} = -\frac{m}{m + 2n}$

$\frac{a^3 + 8}{16 - a^4} : \frac{a^2 - 2a + 4}{a^2 + 4} = \frac{(a + 2)(a^2 - 2a + 4)}{(4 - a^2)(4 + a^2)} : \frac{a^2 - 2a + 4}{a^2 + 4} = \frac{(a + 2)(a^2 - 2a + 4)}{(2 - a)(2 + a)(4 + a^2)} : \frac{a^2 - 2a + 4}{a^2 + 4} = \frac{a^2 - 2a + 4}{(2 - a)(4 + a^2)} * \frac{a^2 + 4}{a^2 - 2a + 4} = \frac{1}{2 - a} * \frac{1}{1} = \frac{1}{2 - a}$

$\frac{x^2 - 12x + 36}{3x + 21} * \frac{x^2 - 49}{4x - 24} = \frac{(x - 6)^2}{3(x + 7)} * \frac{(x - 7)(x + 7)}{4(x - 6)} = \frac{x - 6}{3} * \frac{x - 7}{4} = \frac{(x - 6)(x - 7)}{12}$

$\frac{3a + 15b}{a^2 - 81b^2} : \frac{4a + 20b}{a^2 - 18ab + 81b^2} = \frac{3(a + 5b)}{(a - 9b)(a + 9b)} : \frac{4(a + 5b)}{(a - 9b)^2} = \frac{3(a + 5b)}{(a - 9b)(a + 9b)} * \frac{(a - 9b)^2}{4(a + 5b)} = \frac{3}{a + 9b} * \frac{a - 9b}{4} = \frac{3(a - 9b)}{4(a + 9b)}$