Hello. I made all the wire connections between motors and drivers and even with the board.
I don't know how it is called this board. I can only send you some pics with it.

The problem is that, when I try to connect the board via USB to my laptop with Windows 10, it doesn't make any sound about that the board is connected to the computer. But, on the board is a green light that it is powered on and it works.
I Tried on Mach3 to press some "X+" buttons on MPG mode to test if the motors work, but nothing happened. Also, in section for Ports & Pins, I modified the STEP Pin and DIR pin for X Axis, and enabled them. Even tried to install a driver a RnRMotionControllerECO where I found here, but it is not my board, so I think it exaplains why doesn't work:
https://buildyourcnc.com/item/electronicsAndMotors-electronic-component-breakout-Mach3-USB-Board

Then I tried to connect it to an old computer, windows 7 via Parallel cable, but also, 0 sound and 0 reaction. The software was installed, I enabled Port#1, same pins 2 and 3 for X axis, but nothing happened. Also, I noticed that the green light on board, it turned off after a couple of time (when it was connected with parallel cable).

I don't know what to do, how to set up it so it would work. I tried a lot of things. Did I need the driver for this board? Because I can't find it anywhere and even the name of the board I don't know.

If there are people who now how to make same thing, but with arduino, you would help me a lot if you leave here links with open sources to code and explanation how to connect.

Welcome to the forum.
It would be good if you could resize any future images that you post to 800x600 – it makes them much easier to read. I have resized your current images.

Firstly check that the wire pairs that you have selected for your 8 wire stepper motor are correct – this is important.

The board you have shown is a Parallel Port board which gets its DC power from the USB connection. It does not require a driver. It will not work with Win10 or a laptop so use your old PC with the Parallel Port.
For your motor driver leave the REST terminals unconnected (at present time), connect the CP- and CW- terminals to board GND, then CP+ is the STEP connection and CW+ is the DIRECTION connection. Refer to the Mach3 manual for setting the Ports and Pins accordingly.

Tweakie.

Thank you Tweakie for the edit and for reply.
You could just right-click the image and open into the new window of the browser. In that way, you open in full size, high quality.

Good new.
I have an old computer. On it is installed Windows 7 32bit. The parallel port is also present.
I installed the Mach3 on it. Then the board I connected with parallel cable and also USB cable (it is for 5V power supply).
But, first in the software, I setup pins 2 and 3:
CP- is for Pin 2 (X axis)
CW- is for Pin 3 (X axis)
CP+ and CW+ is for Pin 5V (X axis)

Then I pressed button "Reset" on the software, and with left and right arrow keys, using a multimeter, I tested the parallel port that it is in my computer. It worked. The port was giving 5V when I was pressing the keys.
Then I connected to the board. Using multimeter, I also verified the pin 2 and pin 3 and 5V. It worked also everything.
But, the motors didn't work. Ok, so the driver need to be setup.

The wiring was correct, so I put all the switched to 1 and then in the software Mach3, I setup the green mark for the Step Low and for the Step Port and for the Dir port - I setup 1.

After a new attempt, it finally worked!

Excellent