Question: I'm working on a mechanical device that uses three DSM44 servos, two FEETECH Mini Servo FT1117M, one JX PDI-6208MG Metal Gear Digital Servo, and one DS04-NFC 360 Degree Continuous Rotation Micro Servo Motor with Arduino controller and 6V 8A power supply to the shield.

The DS04-NFC 360 Degree Continuous Rotation Micro Servo Motor in a mechanical device must be kept distant about 8 meters from the controller.

So, I have to find a wire 8-10 meters long and attach connector male/female plugs with a crimping tool, or maybe I can make this with a short male to female lead servo extension cable wire cords, connected to each other to 8-10 meters length long.

I'm not a specialist in motors, powering, and wiring, but as I know, I have to use some kind of servo cable signal booster for such a task.

Can you guide me please, to understand how correctly calculate and provide such a long wire connection and power from the controller shield to a servo motor and separate devices from each other with the required distance

Answer: 
Your DS04-NFC 360 requires PWM signal, GND and 5V/6V supply voltage (<1A current consumption according to Amazon description).

Generally speaking, for power cables, the only thing that matters is the cable section (see AWG wire current chart online). The bigger the section the more current it will handle.
In your case 1A is very small so you don't really have to care.

The other signal is the PWM signal. Problems with digital signal on long distances are both noise (if you have lots of noisy sources like high power motors ... you can twist GND and PWM if this is a problem for you ... see if it helps, or you can use a shielded twisted pair wire with shield connected to GND on both sides ... use that for really noisy environment) and DISTORSION (due to reflection and/or line capacitance : see "characteristic impedance theory" for more information).
Basically you could end up with a signal that really doesn't look like a beautiful square PWM signal anymore. Using simulation tools like LTSpice and their non-ideal transmission line model you can see the effect of an 8-meter cable (if you know the cable specs of course) and experiment some strategies, or you can just play safe and use one of those "servo cable signal booster".
Consider that you are powering five 8 ohm speakers that only draw power when accelerated.

DSM44 servos draw 0.7A on a surge from 6V so the load appears to be about 8 Ohms DC max with a locked rotor but can surge with step changes to this value then decay so the spectrum.

If you understand Woofers audio systems need heavy gauge wire from the power source to push a cone fast with very low resistance wiring that is 0.1% of the source impedance or worst case 1% (Damping Factor =100) . That can be measured by the added % drop in voltage at max current.

let dV/dI=Zs the source impedance of the supply then the loss of the wire degrades the supply's load regulation error and raises it's source impedance.

Given 6V 8A with 1% load regulation error thus Zs= 1% of 6V/8A= 7.5 mohm .

Ideally, your power cable has a local supercap or Lithium or SLA battery near the device with a much smaller impedance than this to compensate for the wire resistance. This resistance will degrade the servo performance under repetitive motions. So lower is better with good damping then you will understand performance will suffer on stiffness and overshoot, resonance, if you use skinny wires to drive the motors.

The control signals should be shielded in twisted pairs isolated from these power wires that can carry fast impulse currents that may result in crosstalk to the control signals if you do not take care of this. (CAT 5 is convenient)

AWG 16 is enough if you have a big supercap near the load. 13.17 mΩ/m \*8 m ~ 105 mohm which drops the steady state voltage by 0.8V but for short duration motions that may be acceptable or not.