You have a 40-pin 3.3V display. You must use 3.3V logic.
Do not believe the "Instructables". You need a proper 40-pin TFT Adapter shield and a Mega2560 board.
It does "look" as if your display only uses an 8-bit interface because the UTFT example uses ILI9325D_8
So you have enough pins on your Nano. But you still need to provide 12 channels of 3.3V logic. e.g. with level-shifter chips or with resistors.
Personally, I find ready-made Adapter shield with ready-made Arduino to be the most reliable.
If you enjoy soldering, you can solder a 20x2 female header to some protoboard. Solder level-shifter i.c.s or resistor voltage dividers. Either solder sockets for the Nano or solder the Nano directly to the protoboard.
Plug your display into the protoboard. And you have a mechanically robust project that is electrically correct too.
David.