I will show you how easy to hack terminals in fallout 4. Usually the passwords are of 4 or 5 letters in novice level and you have maximum 4 attempts to select the correct password, else you the terminal will lock you out for 10 seconds and will restart.

tear

You have to pick a possible password and the terminal will give you “Likeness” number which is a main clue.

Likeness number will say how many letters are in the original password and the letter position. Remember both.

Lets say in above puzzle, we guess TEAR, this  says likeness=1, that is any one letter sure must be in the password. It could be T in position 1 or E in position 2 or A in position 3 or R in position 4.

TEAR
> Likeness = 1

In our second attempt guess, we pick

FIVE
> Likeness = 0

So, we now have 2 clues and we compare letters and letter positions in two words.

On closely looking, the second clue FIVE  has no likeness. This means, our password cant have F in 1st position, I in 2nd positioon, V in 3rd position, E in 4th position.  This also means that our password cant start with F or end with E, likewise with I and V in those positions.

Using these two clues we eliminate the not likely passwords from the screen.

SETS (possible password, also satisfies 2nd clue FIVE and 1st clue TEAR, letter E in correct position)
SEND (possible, also satisfies 1st clue from TEAR, look at E position 2)
PILE (cant be a password, letter I in 2nd position appears our FIVE clue)
PLAY (possible, look at A in 3rd position from TEAR clue,  and 2nd clue rule does not apply )
SASH (cant be password because, it does not have any one of T,E,A,R )
FOND (cant be a password, starts with F, also does not have any one of letters T,E,A,R)
WANT (not possible, because this word does not have correct positions as of TEAR. Letter A not in different positions, which breaks the likeness rule)

Our most likely correct passwords are

SETS, SEND, PLAY

Now we do the third guess attempt and we notice that first 2 possible passwords, starts with SE. Interesting :J. We are almost sure and we try the 3rd attempt.

SETS
> Likeness= 2

For sure, our password is SEND

Please note the original answer in the game, could be different, as my main purpose was to show you the thought process.