a) $\frac{3}{10}\times\frac{4}{9}=\frac{12}{90}=\frac{2}{15}$
b) $2\frac{1}{3}+4\frac{1}{3}=2+\frac{1}{3}+4+\frac{1}{3}=6+\frac{1}{3}+\frac{1}{3}=6\frac{2}{3}$
c) $\frac{6}{5}:\frac{3}{7}=\frac{6}{5}\times\frac{7}{3}=\frac{42}{15}=\frac{14}{5}$
d) $4-\frac{5}{7}=\frac{28}{7}-\frac{5}{7}=\frac{23}{7}$