6 34 = 17 81

$${\frac{6}{17}} \cdot {\frac{34}{81}} = {\frac{6 \cdot 34}{17 \cdot 81}} = {\frac{2 \cdot 3 \cdot 2 \cdot 17}{17 \cdot 3 \cdot 27}} = {\frac{2 \cdot 2}{27}} = {\frac{4}{27}}$$

Ответ: $$\frac{4}{27}$$