To find the undefined value in the equation
\[ 22 = \frac{4 + 5x}{9x - 6}, \]
we need to determine when the expression on the right side becomes undefined. A fraction becomes undefined when the denominator is equal to zero. Thus, we focus on the denominator \( 9x - 6 \) and set it equal to zero:
\[ 9x - 6 = 0. \]
Now, solve for \( x \):
\[ 9x = 6, \] \[ x = \frac{6}{9} = \frac{2}{3}. \]
Therefore, the value that makes the expression undefined is
\[ \boxed{\frac{2}{3}}. \]