To simplify the expression \( \frac{18x^3}{6x^4} \), you can follow these steps:

1. Divide the coefficients (numerical parts):
\[
\frac{18}{6} = 3
\]

2. For the variable parts \( x^3 \) and \( x^4 \), you subtract the exponents (using the rule \( \frac{x^m}{x^n} = x^{m-n} \)):
\[
x^{3-4} = x^{-1}
\]

Putting it all together:
\[
\frac{18x^3}{6x^4} = 3x^{-1}
\]

This can also be written as:
\[
\frac{3}{x}
\]

So, the simplified form of \( \frac{18x^3}{6x^4} \) is \( \frac{3}{x} \) or \( 3x^{-1} \).