To find the exponent that makes the two expressions equivalent, we start with the given expressions:
\[ (16^x)^6 = 16^{18} \]
Using the property of exponents that states \((a^m)^n = a^{m \cdot n}\), we can simplify the left side of the equation:
\[ 16^{6x} = 16^{18} \]
Since the bases on both sides are the same (16), we can set the exponents equal to each other:
\[ 6x = 18 \]
Now, we solve for \(x\) by dividing both sides by 6:
\[ x = \frac{18}{6} = 3 \]
Thus, the exponent that makes the two expressions equivalent is
\[ \boxed{3}. \]