The 6-pin connectors are not for the motherboard (usually, some high end SLI/Crossfire boards take them for PCIe slot power)
If you don't have an 8-pin connector, plug in just the 4-pin where it will fit without forcing it. Some systems will allow booting like this.
However, it is best to get the appropriate cable or an up to date power supply that offers the correct cabling.