Arduino Teensy voltage questions

With my current project, I am planning on using an Arduino Teensy (the smallest board they have) to control two 12V solenoids. I'm planning on running the solenoids off of a 14.8v lipo battery, so I believe I need to use a MOSFET for each solenoid so I don't fry my board.

In the wiring diagram I found online for this (pictured below), the MOSFET gets soldered to the Arduino's ground, but since the ground is shared with the solenoid's ground, wouldn't this send 14.8 volts directly into my Teensy, frying it? I was hoping to use a small 3.4V lipo for the Teensy, but I'm worried about frying the Teensy from the massive brick being used to power the solenoids. Any suggestions or answers are greatly appreciated!

(I am in no way an electrical engineer btw, beginner in programming here)

Connect all Grounds together. It's the positive side you have to worry about

So even though I'm running the ground from a power 3x that of the Teensy's max capability, the ground will be fine?

Grounds are always connected together.

I would be able to just ground the fet to the battery ground as well, correct?

Yes all grounds are connected together.