Hi Anthony,
I believe the reason why your code is not working is because you are trying to compare between the ApprovedBy Keyword object and the AssignedTo Keyword object. These two Keyword objects will never be the same since they are different Keyword Types, even though the value may be the same. What you want to do is compare the values of these Keywords.
However, with your current code, it's possible that you may end up making multiple Keyword removals on a single document. If you happened to have 3 matching values, that means you'll be calling the KeywordModifier.ApplyChanges method 3 times, which become 3 separate calls to the AppServer.
What I would suggest, is to create 3 individual generic list objects (since the values are all going to be a string, all 3 can be a list of string). First 2 list will contain the list of values from the ApprovedBy Keyword and AssignedTo Keyword. The 3rd list will contain the matching value that you will get from comparing the first 2 lists.
After you verify that the 3rd list is not empty, loop through and call the RemoveKeyword method for however many items there are in the 3rd list. After the loop, call the KeywordModifier.ApplyChanges method once, so all the keyword removals you need to apply will only happen once.
EDIT: Now that I look at it, you could do this without having the list objects. You can use the same loop you have, chang the comparison so that it compares the value of the Keyword, and in the loop, call the RemoveKeyword method. You'll also want to set a boolean variable to see if a RemovalKeyword method was called. Then outside of the loop, check the boolean variable, and call the ApplyChanges method.
