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