What do you think that third line is doing right now? It does offer a hint if you run the code though; you should find that it prints the name of the file, then the first line from that file.
So, knowing that, you might want to use a while loop to loop through each line of the file. For each line, you'll want to deal with each word separately. For that, look into split. There's a few things you could do to keep count of how many times each word appears in the file, but I would recommend using a hash. After you've constructed your hash, iterate through each hash key to find the word with the most occurrences and output that value. Do this for each file.
Hashes can be pretty tricky at first, so feel free to check in back here when you reach that part and I'm sure either I or another monk will be glad to help you out with that as well. Good luck!