To solve for \( z \) in the equation
\[ \frac{4z}{9} = 18, \]
follow these steps:
- Multiply both sides by 9 to eliminate the fraction:
\[ 4z = 18 \times 9. \]
Calculating the right side:
\[ 18 \times 9 = 162, \]
so now we have:
\[ 4z = 162. \]
- Next, divide both sides by 4 to solve for \( z \):
\[ z = \frac{162}{4}. \]
Calculating the division:
\[ z = 40.5. \]
Thus, the solution is
\[ z = 40.5. \]