Correct option is (B) \(11\frac{1}{3}\)
\(7\frac{5}{9}\) \(\times\) \(\frac{3}{2}\) = \(\frac{7\times9+5}{9}\) \(\times\) \(\frac{3}{2}\) = \(\frac{63+5}{9}\) \(\times\) \(\frac{3}{2}\) \(=\frac{68}{3\times2}\) \(=\frac{34}3=\frac{33+1}3=11+\frac13\) \(=11\frac13.\)