4. Найдите значение выражения: 1) $$4\frac{2}{3} \cdot 6 - 1\frac{23}{42} \cdot 3\frac{1}{13} + 2\frac{1}{8} \cdot 1\frac{29}{51}$$; 2) $$(5\frac{3}{10} - 3\frac{4}{5} \cdot \frac{13}{38}) \cdot \frac{5}{84} + 2\frac{1}{12} \cdot \frac{4}{15}$$.

Разберем по пунктам.

1. $$4\frac{2}{3} \cdot 6 - 1\frac{23}{42} \cdot 3\frac{1}{13} + 2\frac{1}{8} \cdot 1\frac{29}{51} = \frac{14}{3} \cdot 6 - \frac{65}{42} \cdot \frac{40}{13} + \frac{17}{8} \cdot \frac{80}{51} = \frac{14 \cdot 6}{3} - \frac{65 \cdot 40}{42 \cdot 13} + \frac{17 \cdot 80}{8 \cdot 51} = 28 - \frac{5 \cdot 20}{21} + \frac{17 \cdot 10}{51} = 28 - \frac{100}{21} + \frac{10}{3} = 28 - \frac{100}{21} + \frac{10 \cdot 7}{3 \cdot 7} = 28 - \frac{100}{21} + \frac{70}{21} = 28 - \frac{30}{21} = 28 - \frac{10}{7} = 28 - 1\frac{3}{7} = 26\frac{4}{7}$$.
   Ответ: $$26\frac{4}{7}$$.
2. $$(5\frac{3}{10} - 3\frac{4}{5} \cdot \frac{13}{38}) \cdot \frac{5}{84} + 2\frac{1}{12} \cdot \frac{4}{15} = (\frac{53}{10} - \frac{19}{5} \cdot \frac{13}{38}) \cdot \frac{5}{84} + \frac{25}{12} \cdot \frac{4}{15} = (\frac{53}{10} - \frac{19 \cdot 13}{5 \cdot 38}) \cdot \frac{5}{84} + \frac{25 \cdot 4}{12 \cdot 15} = (\frac{53}{10} - \frac{13}{10}) \cdot \frac{5}{84} + \frac{5 \cdot 1}{3 \cdot 3} = \frac{40}{10} \cdot \frac{5}{84} + \frac{5}{9} = 4 \cdot \frac{5}{84} + \frac{5}{9} = \frac{20}{84} + \frac{5}{9} = \frac{5}{21} + \frac{5}{9} = \frac{5 \cdot 3}{21 \cdot 3} + \frac{5 \cdot 7}{9 \cdot 7} = \frac{15}{63} + \frac{35}{63} = \frac{50}{63}$$.
   Ответ: $$\frac{50}{63}$$.