I don't know why I am getting this error with an iterator. If I didn't have to use the other method I could probably solve this. Thanks for your help. 
package com.codegym.task.task08.task0817;

import java.util.HashMap;
import java.util.Map;
import java.util.Iterator;

/*
We don't need repeats

*/

public class Solution {
    public static HashMap<String, String> createMap() {
        //write your code here

        // initialize hashmap
        HashMap<String, String> people = new HashMap<String, String>();

        // put ten names in the HashMap (last name, first name)
        people.put("Grilli", "Zach");
        people.put("Lawson", "Cole");
        people.put("Rickers", "Cole");
        people.put("Middleton", "Kate");
        people.put("Noonan", "Kate");
        people.put("Fankell", "Jackie");
        people.put("Onassus", "Jackie");
        people.put("Rickersss", "Zach");
        people.put("Lee", "Bruce");
        people.put("Leee", "Bobby");

        // return map
        return people;

    }

    public static void removeFirstNameDuplicates(Map<String, String> map) {
        //write your code here


        // need to create an iterator
        Iterator<Map.Entry<String, String>> iterator = map.entrySet().iterator();

        while(iterator.hasNext()) {

            Map.Entry<String, String> entry = iterator.next();
            String value = entry.getValue();
            removeItemFromMapByValue(map, value);

        }

        // for (Map.Entry<String, String> pair : map.entrySet())
        // {
        //     removeItemFromMapByValue(map, pair.getValue());
        // }

    }

    public static void removeItemFromMapByValue(Map<String, String> map, String value) {
        HashMap<String, String> copy = new HashMap<String, String>(map);
        for (Map.Entry<String, String> pair : copy.entrySet()) {
            if (pair.getValue().equals(value))
                map.remove(pair.getKey());
        }

    }

    public static void main(String[] args) {

        // initialize map
        HashMap<String, String> testMap = createMap();

        // loop through map and print key value pairs
        for (Map.Entry<String, String> pair : testMap.entrySet()) {
            String key = pair.getKey();
            String value = pair.getValue();
            System.out.println(key + ": " + value);
        }

        System.out.println("------------------");

        // call remove method
        removeFirstNameDuplicates(testMap);

        // print out names again
        for (Map.Entry<String, String> pair : testMap.entrySet()) {
            String key1 = pair.getKey();
            String value1 = pair.getValue();
            System.out.println(key1 + ": " + value1);
        }

    }
}