Select the equivalent expression.

To solve the expression \(\left(6^{-4}\cdot 8^{-7}\right)^{-9}\), we can use the properties of exponents.

1. Apply the exponent rule \((a \cdot b)^m = a^m \cdot b^m\):
\[
\left(6^{-4} \cdot 8^{-7}\right)^{-9} = \left(6^{-4}\right)^{-9} \cdot \left(8^{-7}\right)^{-9}
\]

2. Apply the exponent rule \(a^{-m} = \frac{1}{a^m}\) and also \(a^{m \cdot n} = a^{m \cdot n}\):
\[
\left(6^{-4}\right)^{-9} = 6^{36} \quad \text{and} \quad \left(8^{-7}\right)^{-9} = 8^{63}
\]

3. Therefore, we can combine these:
\[
6^{36} \cdot 8^{63}
\]

So, the final equivalent expression is:
\[
6^{36} \cdot 8^{63}
\]

Thus, the answer is **Choice C**: \[6^{36} \cdot 8^{63}\].