Что, собственно, ему не нравится?
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package com.javarush.task.task19.task1906;
/*
Четные символы
*/
import java.util.*;
import java.io.*;
public class Solution {
public static void main(String[] args) throws IOException {
BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
String firstFileName = reader.readLine();
String secondFileName = reader.readLine();
reader.close();
FileReader fileReader = new FileReader(firstFileName);
int countBytes = 0;
char[] cbuf = new char[256];
while (fileReader.ready()) {
countBytes = fileReader.read(cbuf);
}
fileReader.close();
FileWriter fileWriter = new FileWriter(secondFileName, true);
for (int i = 0; i < countBytes; i++) {
if (i%2 == 0) {
fileWriter.write(cbuf[i]);
}
}
fileWriter.close();
}
}