Can I run 12v car fan on 8v
No.

Well yes... for about a second. But it'll only be able to do that trick once.

The 7808 is a linear voltage regulator. The means it takes a higher voltage and reduces it to a lower voltage by shedding the difference in power directly to heat. To figure out how much heat, you can use the simplistic electric power equation:$$P=VI$$

In this case, V is the voltage difference from your car's 12V system to the 8V you want for the fans. Actually, the alternator in your car will hold the voltage at about 14.5 volts. So really it's $$14.5V - 8V = 6.5V$$

And at 20Amps draw:
$$P = V*I = 6.5V * 20A = 130 Watts$$

A typical TO-220 package will raise about 65°C for every Watt of power dissipation (with no heat sink). Most silicon devices can handle up to 150-175°C before they start to melt. 130 Watts times 65°C per Watt raises the temperature over 8000°C. Even if you put a huge heat sink on the TO-220, the best you can get is 5° per Watt. At 130 Watts of dissipation, you're still exceeding 650°C, which will still make it melt very quickly.

To do what you're trying to do probably deserves a question in of itself, so I won't get into details here.