Name the property of multiplication illustrated by $\frac{-4}{3}\times \left(\frac{6}{5}+\frac{8}{7}\right)=\left(\frac{-4}{3}\times \frac{6}{5}\right)+\left(\frac{-4}{3}\times \frac{8}{7}\right).$

Given $\frac{-4}{3}\times (\frac{6}{5}+\frac{8}{7})=(\frac{-4}{3}\times \frac{6}{5})+(\frac{-4}{3}\times \frac{8}{7})$ .
We need to find the property for which it is valid.
We know that for any rational numbers $a,b,c$; the distributive property is given by, 
$a(b+c)=\mathit{ab}+\mathit{ac}$ 

So, $-\frac{4}{3}\times (\frac{6}{5}+\frac{8}{7})=(\frac{-4}{3}\times \frac{6}{5})+(-\frac{4}{3}\times \frac{8}{7}\mathrm{ })$ 

can be illustrated by distributive property considering $a=-\frac{4}{3};b=\frac{6}{5};c=\frac{8}{7}.$
Hence, the distributive property is the correct property used in the given equation.