First, turn these numbers into inproper fractions. Here's how we'd do that:

$$\begin{array}{l} 6\frac{2}{3} = \frac{6\times3+2}{3}=\frac{18+2}{3}=\frac{20}{3}\\\\ 2\frac{2}{5} = \frac{2\times5+2}{5}=\frac{10+2}{5}=\frac{12}{5}\\\\ 3\frac{3}{8} = \frac{3\times8+3}{8}=\frac{24+3}{8}=\frac{27}{8} \end{array}$$

Now we get:

$$\frac{20}{3}\times\frac{12}{5}\times\frac{27}{8}$$

This can simplified, so we get:

$$\frac{1}{1}\times\frac{2}{1}\times\frac{27}{1}$$

$$\frac{1\times2\times27}{1\times1\times1}$$

$$\frac{54}{1}$$

$$54$$