We start with the expression given:
\[ \frac{8^?}{8^4} = 8^{15} \]
Using the properties of exponents, particularly the property that states \(\frac{a^m}{a^n} = a^{m-n}\), we can rewrite the left side of the equation:
\[ 8^{? - 4} = 8^{15} \]
Since the bases are the same (both are base 8), we can set the exponents equal to each other:
\[ ? - 4 = 15 \]
To find the missing number (which we denote as \( ? \)), we add 4 to both sides:
\[ ? = 15 + 4 \]
Calculating that gives:
\[ ? = 19 \]
Therefore, the missing number is
\[ \boxed{19} \]