How to connect an old motherboard with a 12 pins power connector?

EDIT: I appreciate all the thumbs ups, but as other users have pointed out this is likely not an AT connector. After doing more research, my best suggestion to the OP is to purchase the original part number item to insure compatibility with this system. There are no second chances, once the wrong power supply is plugged in, the motherboard is toast.

It appears, based on research, that this system is a Compaq Presario 22xx series. The specs of that series, and references to the original power supply part number suggest that this is an ATX style power supply. The extra 6-pin plug is typically an auxiliary connection. However, it is highly likely, as suggested by other commentators that this is a completely proprietary power supply. A lot of manufacturers are guilty of creating non-standard systems around this era. I cannot find any standard power supplies that used 12 pin AT/PC style power connectors and a 6-pin auxiliary connector. What is for sure, is that this power supply (not clearly seen in the OP's photo) is also proprietary in shape and size:

So, I have left the original message below, but I think it is prudent to not take chances given the sensitive nature of this repair. Just spend the money on getting the exact original part number.

----- ORIGINAL ----- The connector on your motherboard is an AT connector. The power supply you are trying to hook up is an ATX connector.

You'll need to buy an AT power supply. When you hook it up make sure you attach the two motherboard power connectors with the black wires next to each other.

http://wiki.robotz.com/index.php/PC_Power_Supply_Voltage_Data_and_Connector_Types

Now, I have to ask - What are you doing with this computer from 20+ years ago?

This is a Compaq Presario desktop power supply. (That is what the Compaq spares number indicates.) Compaq was notorious for inventing their own slightly non-standard wiring configurations for power supplies and motherboards. It is neither an AT or an ATX power supply.

You can find reconditioned units but they are expensive here are a few I found.

Memory 4 Less
Impact Computers

As mentioned in the other answer that is an old AT style power connector.

It is possible to connect an ATX power supply using an adapter but there are a couple of caveats.

1. Your system may need -5V which modern ATX PSUs don't have (some but not all older ones do)
2. AT power supplies are not controlled by the motherboard but by a seperate power switch. The adapter is likely to have a pair of wires for connecting to your power switch. Depending on your case design you may be able to hook up the existing power switch or you may need to fit a new one to the case somehow.