To solve the equation \( 6^{-4} \div 6^{?} = 6^{13} \), we can use the properties of exponents.
First, recall that dividing two powers with the same base results in subtracting the exponents:
\[ 6^{-4} \div 6^{?} = 6^{-4 - ?} \]
Now we can set the left side equal to the right side:
\[ 6^{-4 - ?} = 6^{13} \]
Since the bases are the same (both are base 6), we can set the exponents equal to each other:
\[ -4 - ? = 13 \]
Now, solve for \( ? \):
\[ -? = 13 + 4 \]
\[ -? = 17 \]
Multiply both sides by -1:
\[ ? = -17 \]
Thus, the missing value is
\[ \boxed{-17} \]