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To find the undefined value for the equation \( 22 = \frac{4 + 5x}{9x - 6} \), we should determine when the denominator is equal to zero, as this will make the expression undefined.
1. Set the denominator equal to zero:
\[
9x - 6 = 0
\]
2. Solve for \( x \):
\[
9x = 6
\]
\[
x = \frac{6}{9}
\]
\[
x = \frac{2}{3}
\]
Thus, the undefined value for the given equation is:
\[
\boxed{\frac{2}{3}}
\]