2. (1$$\frac{9}{16}$$ * 3$$\frac{1}{5}$$ + 1$$\frac{2}{3}$$ - 9 : 2$$\frac{2}{5}$$) : 17$$\frac{7}{12}$$ - (6$$\frac{1}{3}$$)

Let's solve this expression step by step: 1. Convert mixed numbers to improper fractions: $$1\frac{9}{16} = \frac{1 \cdot 16 + 9}{16} = \frac{25}{16}$$ $$3\frac{1}{5} = \frac{3 \cdot 5 + 1}{5} = \frac{16}{5}$$ $$1\frac{2}{3} = \frac{1 \cdot 3 + 2}{3} = \frac{5}{3}$$ $$2\frac{2}{5} = \frac{2 \cdot 5 + 2}{5} = \frac{12}{5}$$ $$17\frac{7}{12} = \frac{17 \cdot 12 + 7}{12} = \frac{211}{12}$$ $$6\frac{1}{3} = \frac{6 \cdot 3 + 1}{3} = \frac{19}{3}$$ 2. Calculate the expression inside the parentheses: $$(\frac{25}{16} \cdot \frac{16}{5} + \frac{5}{3} - 9 : \frac{12}{5})$$ 3. Perform multiplication and division from left to right: $$\frac{25}{16} \cdot \frac{16}{5} = \frac{25 \cdot 16}{16 \cdot 5} = \frac{25}{5} = 5$$ $$9 : \frac{12}{5} = 9 \cdot \frac{5}{12} = \frac{9 \cdot 5}{12} = \frac{45}{12} = \frac{15}{4}$$ 4. Substitute the values back into the parentheses: $$(5 + \frac{5}{3} - \frac{15}{4})$$ 5. Find a common denominator for the fractions, which is 12: $$5 + \frac{5 \cdot 4}{3 \cdot 4} - \frac{15 \cdot 3}{4 \cdot 3} = 5 + \frac{20}{12} - \frac{45}{12}$$ 6. Perform the addition and subtraction: $$5 + \frac{20 - 45}{12} = 5 - \frac{25}{12} = \frac{5 \cdot 12}{12} - \frac{25}{12} = \frac{60}{12} - \frac{25}{12} = \frac{35}{12}$$ 7. Now, calculate the expression outside the parentheses: $$\frac{35}{12} : (\frac{211}{12} - \frac{19}{3})$$ 8. Find a common denominator for the subtraction: $$\frac{211}{12} - \frac{19 \cdot 4}{3 \cdot 4} = \frac{211}{12} - \frac{76}{12} = \frac{211 - 76}{12} = \frac{135}{12}$$ 9. Perform the division: $$\frac{35}{12} : \frac{135}{12} = \frac{35}{12} \cdot \frac{12}{135} = \frac{35 \cdot 12}{12 \cdot 135} = \frac{35}{135} = \frac{7}{27}$$ So, the final answer is: $$\frac{7}{27}$$