If my mother gives me $20,000, how much would the penalty be?

Here is a very good thread on this subject.
The short answer is if your mom has $20,000 to give away she needs to see an elder attorney before doing so in order to understand the ramifications for her future.

https://www.agingcare.com/questions/protect-mothers-savings-when-goes-into-nursing-home-197284.htm

Are you talking about the IRS gift tax, or are you asking about the Medicaid penalty if she requires nursing home care?

There is a formula that determines how many days your mother will have to self-pay before she is eligible for Medicaid. I don't know it, but maybe someone can work it out for you. What state would her nursing home be in?

20,000.