The white wire that is behind the white wire on the four wire plug that I am removing for the three prong plug.... can that be used for the ground wire?


No. It is likely that that other white wire goes to the controls of the dryer, which normally requires 120 volts rather than 240. Leave it where it is and add another ground wire to the frame.

Updated on January 8, 2018

Original Article:

How to Change a 4-Prong Dryer Cord and Plug to a 3-Prong
By Dan Harmon