20 pin --> 24 pin adapter.
Long ago, they had 20 pin PSU connectors and everything was powered from the motherboard. Components became more power hungry.
PSU connectors went to 24 pins. The four extra pins were one each 3.3, 5, and 12 volts and a ground. CPU's got their own 12 volt connector and power through the main power plug dropped.
Video cards got bigger and got their own 12 volt power connectors and 5 volt power through the main power plug dropped.
RAM went from SDRAM (3.3 volts) to DDR2 and DDR3 (1.65 - 2.2 volts) and 3.3 volt power through the main power plug dropped.
You don't need an adapter. An adapter will not magically increase the amount of power the PSU can provide.
Just use the 20 pin socket. If your PSU can provide enough 12 volt current, you will be OK. If it doesn't work, you need a more modern PSU with a greater 12 volt capacity.