To solve the equation \((8^3)^n = 8^{12}\), we can use the property of exponents that states \((a^m)^n = a^{m \cdot n}\).
Applying this property, we have:
\[ (8^3)^n = 8^{3n} \]
Thus, we can rewrite the equation as:
\[ 8^{3n} = 8^{12} \]
Since the bases are the same, we can equate the exponents:
\[ 3n = 12 \]
Now, we solve for \(n\):
\[ n = \frac{12}{3} = 4 \]
Therefore, the value of \(n\) is:
\[ \boxed{4} \]