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To find the undefined value for the equation \( 22 = \frac{4 + 5x}{9x - 6} \), we need to identify when the denominator equals zero, as that is when the expression is undefined.
The denominator is \( 9x - 6 \). We set this equal to zero and solve for \( x \):
\[
9x - 6 = 0
\]
Adding 6 to both sides gives:
\[
9x = 6
\]
Now, dividing both sides by 9:
\[
x = \frac{6}{9}
\]
We can simplify \( \frac{6}{9} \):
\[
x = \frac{2}{3}
\]
Thus, the undefined value is:
\[
\boxed{\frac{2}{3}}
\]