\(\frac{34}{11}\cdot\frac{1269}{46}\cdot\frac{23}{17}\cdot\frac{22}{9}\)
\(=\frac{34\cdot1269\cdot23\cdot22}{11\cdot46\cdot17\cdot9}\)
\(=\frac{17\cdot2\cdot141\cdot9\cdot23\cdot11\cdot2}{11\cdot23\cdot2\cdot17\cdot9}\)
\(=\frac{2\cdot141\cdot2}{2}\)
\(=141\cdot2\)
\(=282\)