problem with connecting the Arduino with 12V electric door strike
Your circuit schematic is a mess and you don't explain why you think a little 9 V battery will energise a 12 V relay or solenoid in the door strike.

First thing is get a 12 V PSU with a current rating >= the sum of the currents required by the relay and the solenoid.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Relay control for solenoid operation.

How it works


When D8 goes high current will flow through R1 to the base of Q1 turning it on.
RLY1 will turn on.
The contact of RLY1 will energise the solenoid.


Make sure you connect the 5 V ground and your 12 V ground.

Testing


Disconnect R1 from D8 and connect it to +5 V. The relay and solenoid should operate.
Reconnect and you can start testing your code. You should hear the relay click.


The door strike datasheet shows the following data:



Figure 2. Coil data.

This clearly shows that there is a 26 Ω coil and that it will draw 450 mA, presumably, at 12 V (mid 10 - 14 V DC). (I think you have represented the coil with a switch in your diagram.)

The Circuit Type row is showing you that the circuit is powered from a normally open contact (as shown in my Figure 1) so it consumes no power when locked. You energise the coil briefly to unlock. Note that if you have a power failure you will be unable to unlock the door with this device.