In a galaxy far away...
“Forget about a coin mech”
Start on your basic skills.
Put two buttons on a breadboard.
Learn how to detect a press on button #1
Once you have that sorted, figure out how to count the number of pushes on button #2
A little while later, see if you can clear the press count, and enable button #2 with button #1
Show us that code. There are a number of tutorials and intro sketches to do all that. You just need to look.
Arduino button press
Arduino counting pulses
Once you have the button/pulse detection working reliably, leave it alone and display that activity on the LCD
Once that’s done, we can help you sort/count specific denominations
This is called modular programming.
Bottom-Up, so you know the fundamentals will work when you need them.
The way you’ve been asking for help is going to (already has) made work frustrating and hard for you, because nothing just ‘falls into place by itself’.
Writing software (and building hardware) is a skilled, lengthy and considered process. No shortcuts unless you’re using LEGO mindstorms. which could be one way to avoid learning Arduino methods.