\(3:\frac{9}{4}=\frac{3}{4}.\left(6x\right)\Rightarrow\frac{3}{4}.\left(6x\right)=3.\frac{4}{9}\Rightarrow\frac{3}{4}.\left(6x\right)=\frac{4}{3}\Rightarrow6x=\frac{4}{3}:\frac{3}{4}\Rightarrow6x=\frac{4}{3}.\frac{4}{3}\Rightarrow6x=\frac{16}{9}\Rightarrow x=\frac{16}{9}:6\Rightarrow x=\frac{16}{9}.\frac{1}{6}\Rightarrow x=\frac{16}{54}=\frac{8}{27}\)