Thank you for using the site. I'll be happy to help you with this.
There are a few ways that you can approach this, depending on the resources available to you.
If you have Excel, you can enter "=normsinv(0.20)" into a cell, which will give you the result z = -0.8416.
If you have tables, then you would locate the entry in the table that is closest to 0.20 and read off the corresponding z value. You may need to interpolate between values to get an accurate answer. Most tables of the normal distribution, however, give the right side tail area. You can use the symmetry of the distribution though to solve the problem. Find the z value that corresponds with a right tail area of 0.20, and then add a negative sign to the z value to get the final answer.
You can also use a statistical calculator. I like the one at this site. Simply click the button under the "Left tail" graph, enter 0.20 in the "probability" box, and then click the arrow that points from the probability box toward the z-value box. The result is -0.8416.
Please feel free to ask if you have any additional questions about this.