Six machines, working at the same constant rate together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate are needed to complete the job in 8 days?

What I did (and where am I wrong?):

each machine does "2" of the job in 6 days (since each machine does 2 parts of the job). so rate of each machine is 2/6 which is 1/3.

(1/3)*6 +(1/3) *x = 1/8.

I understand I'm taking out the rate wrong...but what else should it be? Rate is always 1/ work done in a day.... so 12/6=2, even if i use rate of 1/2, the answer is still wrong. Im very confused.

Thanks a lot!

Answer is 3