We have that the total gross pay is $14,600.
The state tax rate is 3.5%.
First, we need to find the 3.5% of $14,600:

This is the total value of tax in a year. Then, to find how much she pays we need to divide this amount by 12 (number of months of the year). Then, we have:

Therefore, she needs to pay $42.58 a month in state taxes.