Hello, usre123!

Your reasoning is faulty . . .

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?

I baby-talked my way through the problem like this . . .

That final fraction equalsone.wholejob

. . Hence:-

Nine machines are required.

Therefore, 3 additional machines are needed.