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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
\[
\boxed{\frac{2}{3}}.
\]