$6b^2 * \frac{5b^2 - 4}{3} + 20b * \frac{3b - 2b^3}{4} = 2b^2(5b^2 - 4) + 5b(3b - 2b^3) = 10b^4 - 8b^2 + 15b^2 - 10b^4 = (10b^4 - 10b^4) + (15b^2 - 8b^2) = 0 + 7b^2 = 7b^2$

$14m * \frac{m + n}{7} - \frac{m - n}{8} * 16n - 2(m^2 + n^2) = 2m(m + n) - 2n(m - n) - 2m^2 - 2n^2 = 2m^2 + 2mn - 2mn + 2n^2 - 2m^2 - 2n^2 = (2m^2 - 2m^2) + (2mn - 2mn) + (2n^2 - 2n^2) = 0 + 0 + 0 = 0$