Usually, the tables for z-scores report the value at the left of given z-values. Then we can rewrite the question.
When the z-value has 67.4% of the area distribution it means that at its left we have: 100% - 67.4% = 32.6% of the area.
Now we just need to read the z-value table and find the z-score associated with a probability of 0.326. Reading from the table, the z value is approximately -0.45.