To solve the equation \((16^x)^6 = 16^{18}\), we can use the property of exponents that states \((a^m)^n = a^{m \cdot n}\).
Applying this property to the left side of the equation, we get:
\[ (16^x)^6 = 16^{6x} \]
So we can rewrite the equation as:
\[ 16^{6x} = 16^{18} \]
Since the bases are the same (both are base 16), we can set the exponents equal to each other:
\[ 6x = 18 \]
Now, to solve for \(x\), we divide both sides by 6:
\[ x = \frac{18}{6} = 3 \]
Thus, the exponent that makes the two expressions equivalent is:
\[ \boxed{3} \]