\(2\dfrac{13}{2}-\dfrac{7}{15}+3\dfrac{14}{27}-\dfrac{8}{15}\)
\(=\dfrac{17}{2}+\dfrac{95}{27}-\left(\dfrac{7}{15}+\dfrac{8}{15}\right)\)
\(=\dfrac{459}{54}+\dfrac{190}{54}-1\)
\(=\dfrac{649}{54}-1\)
\(=\dfrac{649}{54}-\dfrac{54}{54}\)
\(=\dfrac{595}{54}\)