Some rough power calculations using Ohm's Law (P = IE):
Solar panel, 20V 0.8A:
$$20 * 0.8 = 16W$$
Fans, 2 at 12V 0.4A:
$$12 * 0.4 * 2 = 9.6W$$
Pump, 6V 0.1A:
$$6 * 0.1 = 600mW$$
Total power needed:
$$9.6 + 0.6 = 10.2W$$
So far, so good. You have enough power to drive the loads. However, you need to convert 20V to 12V and 6V. Voltage conversions are not 100% efficient, so you will lose some power doing so, but you have about 5W overhead so this should not be a problem.
One way to lower the voltage would be with inexpensive linear voltage regulators, but these are not the most efficient, and many have a maximum input voltage of 18V.
That being the case, I would look for a DC-DC Buck converter. They are more expensive, but offer higher efficiency because they use switching instead of converting excess voltage to heat.
You can build or buy (such as this $5 module on eBay). I am not sure I would trust the eBay units, so I would be interested in building my own. However you might try your luck given the low price.
Keep in mind that the solar panel output will vary (with cloud cover, sun angle, etc.) so you might want to consider using batteries as a buffer to ensure that you aren't trying to operate things with insufficient power (for example, if someone shades the panel). Another option might be to add a circuit which disables the output if the solar panel isn't producing enough. There are lots of resources on the internet about charging batteries from solar panels, so I won't go into detail on that.