The show promoters are probably asking for your sales and use tax ID number.
If you plan to sell at only one or two shows each year, you should be able to
obtain a temporary sales tax permit for each show that will cover the dates
of the specific show. Many states have the form online so you can print a
copy. Check the web site of your state department of revenue or taxation.

This isn't really the answer to your question, but you already have a tax
ID... your social security number.

Also, you can if you've got a business go online to the www.irs.gov website
and (during most hours of workdays) instantly get an employer identification
number (or EIN) which also works as a tax ID.

I would not be surprised, though, if what you're really referring to or
wondering about is something like a state of Michigan ID number--perhaps
something needed for dealing with sales taxes, etc.