What is the most profitable way to use Arduino?

Find a jurisdiction where cannabis is still illegal and consult for black market growers who need lights and watering automated. They may be willing to pay for remote control and monitoring, too. I recommend against that because it generates evidence; but the customer is always right, right?

Profitable at long term,for me, teaching my children how computers work

There's probably an ATmega328P chip somewhere in the U.S. Mint's workflow.[1] I'm personally not willing to risk whatever list you get put on by googling terms that might verify that.

Edit: "Fun Fact! Coins and paper bills aren’t made by the same agency. The Bureau of Engraving and Printing (BEP) makes paper money."

1.https://www.usmint.gov/learn/kids/about-the-mint

for learning, why to emphasis on profits?