Find the z value to the left of the mean so that 64.7% under the distribution curves lies to the right of it.

What is 64.7%? It's a probability of 64.7/100 = 0.647.

Now, sketch the z distribution curve, and estimate the location of the z value. Obviously it's a negative number.

Now, to what z value does the probability of 0.647 belong to in your z table?

Depending on what type of z table you're using, you'll have a certain value of z. Do the necessary changes if needed to get the z value you're looking for.

Since 64.7% lies to the right, then 1-.647=.353 must lie to the left.
Look up .353 in the z-table and find its corresponding z value.