how do I control a relay and how 6Volt intention piloting equal to 10V. how can I do?

Must first know if the voltage available is continuous or alternating.
In the case of voltage + simple solution is to insert a resistor in series with the relay coil and food between the free end of the resistor and the free end of the coil of the relay.

value of the resistor is obtained by the following calculation

Rc = (Vcc-Vr) / (Vr / Rb)

where
Rc is the value of the resistor connected in series in Ohms
Vcc is the voltage available in volts (10V)
VR is the voltage of the relay in Volt (6V)
Rb is the resistance of the coil of the relay (usually located on the relay with the voltage)

The resistor must be sized not only for the value of resistance for power dissipation that takes him to heat up.
The power dissipated by the revenue report

Pd = Vc * Vc / Rc

with
Pd in Watts
Vc in volts (Vc = Vcc-Vr)

Please note that if the relay should remain energized + of a few seconds per minute, the energy dissipated on the resistor will inevitably lead to warm up then it is good practice to predict one that has a power dissipation of at least double that from the report above ( therefore greater than 2 * Pd).

The case of supply of alternating voltage varies little but the face if it's your problem.

Hello

Antani

another idea is to put 5 diodes in series with the relay with a fall of 0.8 volts to create a diode drop of 4 volts.

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Control relays with 6-volt drive voltage to 10 volts