To simplify the expression \((-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \div \left(\frac{7}{15}\right)\), we can follow two main steps: multiplication and division.
First, let's rewrite the division as multiplication by the reciprocal:
\[ (-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \times \left(\frac{15}{7}\right) \]
Now we can calculate the product step by step.
- Calculate the product of the first two numbers:
\[ (-4) \times \left(-\frac{3}{4}\right) = \frac{12}{4} = 3 \]
- Now multiply this result by \(\left(\frac{7}{5}\right)\):
\[ 3 \times \left(\frac{7}{5}\right) = \frac{21}{5} \]
- Finally, multiply this result by \(\left(\frac{15}{7}\right)\):
\[ \left(\frac{21}{5}\right) \times \left(\frac{15}{7}\right) = \frac{21 \times 15}{5 \times 7} = \frac{315}{35} \]
- Simplifying \(\frac{315}{35}\):
\[ \frac{315 \div 35}{35 \div 35} = \frac{9}{1} = 9 \]
Thus, the final result of the expression is:
\[ \boxed{9} \]