\(1\dfrac{3}{15}-3.\left|\dfrac{-4}{9}\right|+\sqrt{\dfrac{16}{25}}\)
\(=\dfrac{6}{5}-3.\dfrac{4}{9}+\dfrac{4}{5}\)
\(=\dfrac{6}{5}-\dfrac{4}{3}+\dfrac{4}{5}\)
\(=\left(\dfrac{6}{5}+\dfrac{4}{5}\right)-\dfrac{4}{3}\)
\(=\dfrac{10}{5}-\dfrac{4}{3}\)
\(=2-\dfrac{4}{3}=\dfrac{2}{3}\)