I have no doubt this circuit will work, although it's a bit of overkill for the application. I would have used a simpler circuit.
The LM7808 device is an 8 volt regulator. The 1N4002 diode provides a .6 volt drop, and the base-to-emitter junction of the 2N5881 drops the voltage another .6 volts to get you to 6.8 volts. The 2N5881 has a maximum collector current of 15 amps, so you have up to 15 amps available to drive your gauges. Note that at 15 amps, the 2N5881 will need to dissipate 120 watts, so you'll need a healthy heat sink to do that. I would ditch the two capacitors from this design (potential failure points that don't do much), but otherwise it looks fine.
Note that the TO-3 package of the 2N5881 is a bit of a pain to work with. If you can get by with only 1 amp, the LM7808 can do that on its own. You can put a pair of 1N4002 diodes in series with the voltage regulator output to get your voltage drop.
Another solution is to use an LM350K adjustable regulator, which can provide up to 3 amps, requiring only a couple of resistors in addition to the VR. The LM350K is a TO-3 package. In a TO-220 package you can get the LM317 which is good for 1.5 amps.
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