To solve the expression \(6^{-6} \times 6^{2}\), we can use the properties of exponents.
When multiplying two expressions with the same base, we can add their exponents:
\[ 6^{-6} \times 6^{2} = 6^{-6 + 2} = 6^{-4} \]
Now, writing \(6^{-4}\) in positive exponent form gives us:
\[ 6^{-4} = \frac{1}{6^{4}} \]
Finally, \(6^{4}\) can be calculated as:
\[ 6^{4} = 6 \times 6 \times 6 \times 6 = 1296 \]
Thus,
\[ 6^{-4} = \frac{1}{1296} \]
The final answer is:
\[ \frac{1}{1296} \]