To solve for \( x \) in the equation
\[ \frac{4x}{9} = 18, \]
you can start by multiplying both sides of the equation by 9 to eliminate the fraction:
\[ 4x = 18 \times 9. \]
Calculating \( 18 \times 9 \):
\[ 18 \times 9 = 162. \]
So, the equation simplifies to:
\[ 4x = 162. \]
Next, divide both sides by 4 to isolate \( x \):
\[ x = \frac{162}{4}. \]
Calculating \( \frac{162}{4} \):
\[ x = 40.5. \]
Thus, the solution is
\[ x = 40.5. \]