Я проверил,вроде все как надо выводит...
package com.javarush.task.task19.task1906;
import java.io.*;
import java.util.ArrayList;
/*
Четные символы
*/
public class Solution {
public static void main(String[] args) throws Exception{
BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
String firstFileName = reader.readLine();
String secondFileName = reader.readLine();
reader.close();
FileReader fileReader = new FileReader(firstFileName);
FileWriter fileWriter = new FileWriter(secondFileName);
int count = 1;
while (fileReader.ready() && count % 2 == 0) {
if(count % 2 == 0) {
fileWriter.write(fileReader.read());
}
else{
fileReader.read();
}
count++;
}
fileReader.close();
fileWriter.close();
}
}