How much is an old Kenmore sewing machine model number 566 3242 worth?

Roughly about $40 if the cabinet's included ... really, it's usually whatever the market will bear. And since you can usually buy a new machine with the same or more features for about $100, most people choose to buy new.

OTOH, price is also driven by sentimental or antique value ... in this case, not much. :( Just to set the record, the 5186 refers to the electric motor on the sewing machine, most machines with this motor are not so old. They date to around early 1970s.