let's firstly convert the mixed fractions to improper fractions and then multiply.
[tex]\bf \stackrel{mixed}{4\frac{3}{5}}\implies \cfrac{4\cdot 5+3}{5}\implies \stackrel{improper}{\cfrac{23}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{23}{5}\cdot \cfrac{2}{3}\implies \cfrac{23\cdot 2}{5\cdot 3}\implies \cfrac{46}{15}\implies 3\frac{1}{15}[/tex]
