Simplify 2a(4b2) + 3b(-2ab) / 2ab2 and -3a3 x (2b3 - 6b3) - (-3ab)3 / -3a2b. Calculate -6 + sqrt(4x(4-9)) - (-5), -32 x sqrt(9+16) + -2 - 6, and sqrt(16) - sqrt(144).

Here are the solutions to the problems.

2.1.1 Simplify: $\frac{2a(4b^2) + 3b(-2ab)}{2ab^2}$

Step 1: Expand the terms in the numerator. $2a(4b^2) = 8ab^2$ $3b(-2ab) = -6ab^2$

Step 2: Substitute the expanded terms back into the expression. $\frac{8ab^2 - 6ab^2}{2ab^2}$

Step 3: Combine like terms in the numerator. $\frac{2ab^2}{2ab^2}$

Step 4: Simplify the fraction. $1$ The final answer is $\boxed{1}$.

2.1.2 Simplify: $\frac{-3a^3 \times (2b^3 - 6b^3) - (-3ab)^3}{-3a^2b}$

Step 1: Simplify the expression inside the first parenthesis in the numerator. $2b^3 - 6b^3 = -4b^3$

Step 2: Calculate $(-3ab)^3$. $(-3ab)^3 = (-3)^3 a^3 b^3 = -27a^3b^3$

Step 3: Substitute these simplified terms back into the numerator. $-3a^3 \times (-4b^3) - (-27a^3b^3)$

Step 4: Perform the multiplication and simplify the double negative in the numerator. $12a^3b^3 + 27a^3b^3$

Step 5: Combine like terms in the numerator. $39a^3b^3$

Step 6: Write the full expression with the simplified numerator. $\frac{39a^3b^3}{-3a^2b}$

Step 7: Divide the terms. $-13a^{3-2}b^{3-1}$ $-13ab^2$ The final answer is $\boxed{-13ab^2}$.

2.2.1 Calculate: $-6 + \sqrt{4 \times (4-9)} - (-5)$

Step 1: Simplify the expression inside the parenthesis. $4-9 = -5$

Step 2: Substitute this value back into the square root. $-6 + \sqrt{4 \times (-5)} - (-5)$ $-6 + \sqrt{-20} - (-5)$

Step 3: Simplify $\sqrt{-20}$. $\sqrt{-20} = \sqrt{20}i = \sqrt{4 \times 5}i = 2\sqrt{5}i$

Step 4: Substitute the simplified square root and the double negative. $-6 + 2\sqrt{5}i + 5$

Step 5: Combine the real number terms. $-1 + 2\sqrt{5}i$ The final answer is $\boxed{-1 + 2\sqrt{5i}}$.

2.2.2 Calculate: $-3^2 \times \sqrt{9+16} + \frac{-3 \times 2^3}{-2-6}$

Step 1: Calculate $-3^2$. $-3^2 = -(3^2) = -9$

Step 2: Calculate $\sqrt{9+16}$. $\sqrt{9+16} = \sqrt{25} = 5$

Step 3: Calculate $2^3$. $2^3 = 8$

Step 4: Calculate the denominator of the fraction. $-2-6 = -8$

Step 5: Substitute these values back into the expression. $-9 \times 5 + \frac{-3 \times 8}{-8}$

Step 6: Perform the multiplication in the first term and the multiplication in the numerator of the fraction. $-45 + \frac{-24}{-8}$

Step 7: Perform the division in the fraction. $-45 + 3$

Step 8: Perform the final addition. $-42$ The final answer is $\boxed{-42}$.

2.2.3 Calculate: $\sqrt{16} - \sqrt{144}$

Step 1: Calculate $\sqrt{16}$. $\sqrt{16} = 4$

Step 2: Calculate $\sqrt{144}$. $\sqrt{144} = 12$

Step 3: Perform the subtraction. $4 - 12$ $-8$ The final answer is $\boxed{-8}$.