Hacking terminals in Fallout 3 & 4 is now easier than ever. This page will help you as much as possible to get to the final answer.
It works as follows. First, you have to give all the possible words. Just type them in the big text box, separated by spaces or enters. Once you’ve done that, click on “Hack”. It will show you the words that could be the password, which means that initially it will show all of them. Pick a word, and choose it to guess the password in the game. When the terminal answers with the number of correct letters, click on that number behind the word you chose. The display will be updated to reflect the words that you can still choose from. Keep going until you’ve hacked the terminal.
I published the algorithm used for hacking as a Python script back in 2008.
Enter all the potential passwords you see in the terminal's memory dump, separated by spaces:
Use any of these words to guess the password. When the terminal tells you how many letters you got correct, click on that number behind the word you chose.
We suggest trying either or
Congratulations! You have found the password:
You have tried some passwords, but they do not match any known word. Check that you didn't make any mistakes, and if you didn't, log out of the terminal and try again.
Here you see which passwords you've tried already.