I am trying to figure out how I can make my script verify a "password"
You get a String, you know how to check a String's length, so solved.
is between 6 and 10 characters long
Yep, your for-loop idea is good here. Character class has methods that may help you here.
contains at least one letter, and contains at least one digit
In other words, this loops for an unknown number of times until some conditions are true. Which is the best type of loop for this? You should then think what code should go into the loop (hint: most of it). You might want to have a boolean variable for each condition above (lengthOK, containsChar, containsLetter) and checking that all are true before exiting your loop.
in addition to prompting the user until the password is ok.
hint: don't forget that you compare Strings with the equals method not with ==.
After that I need to make sure that the password is then entered properly twice.
I'd scrap this and work out the logic first on paper before trying to type in the code. Otherwise you'll end up with a hit-or-miss type of program.
This is what I have so far:...