Hi! "would far rather" is a variation of "would rather..." Both express that you prefer to do something over something else, only the latter does it with more emphasis.

Examples:

"I would rather be my own boss than work for someone else." This means that you prefer to be independent, and you would choose this over being an employee.

If you say "I would far rather be my own boss than work for someone else." then you are expressing a stronger (or a very strong) preference to being your own boss over being employed. It means you really, really would prefer the first option over the second one.

If you have any doubts, don't hesitate to ask.

Good luck!