Connecting Peltier module to Arduino Nano
I prepared a little circuit that should help you safely connect the Peltier module to Arduino. It uses a single n-channel MOSFET and 1K resistor.

I couldn't find any Peltier in Tinkercad so instead I used a simple light bulb. (In previous version of this answer I used a DC motor, but it was not a good replacement for Peltier module)

When Arduino Pin12 is HIGH light is bright (high current flows through it just like it should through the Peltier) when Pin12 is LOW light bulb goes dark (no current is flowing)